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standard library package ISQMechanics {
doc
/*
* International System of Quantities and Units
* Generated on 2022-08-07T14:44:27Z from standard ISO-80000-4:2019 "Mechanics"
* see also https://www.iso.org/obp/ui/#iso:std:iso:80000:-4:ed-2:v1:en
*
* Note 1: In documentation comments, AsciiMath notation (see http://asciimath.org/) is used for mathematical concepts,
* with Greek letters in Unicode encoding. In running text, AsciiMath is placed between backticks.
* Note 2: For vector and tensor quantities currently the unit and quantity value type for their (scalar) magnitude is
* defined, as well as their typical Cartesian 3d VectorMeasurementReference (i.e. coordinate system)
* or TensorMeasurementReference.
*/
private import ScalarValues::Real;
private import Quantities::*;
private import MeasurementReferences::*;
private import ISQBase::*;
/* Quantity definitions referenced from other ISQ packages */
private import ISQThermodynamics::EnergyValue;
/* ISO-80000-4 item 4-1 mass */
/* See package ISQBase for the declarations of MassValue and MassUnit */
/* ISO-80000-4 item 4-2 mass density, density */
attribute def MassDensityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-2 mass density, density
* symbol(s): `ρ`, `ρ_m`
* application domain: generic
* name: MassDensity
* quantity dimension: L^-3*M^1
* measurement unit(s): kg*m^-3
* tensor order: 0
* definition: quantity representing the spatial distribution of mass of a continuous material: `ρ(vec(r)) = (dm)/(dV)` where `m` is mass of the material contained in an infinitesimal domain at point `vec(r)` and `V` is volume of this domain
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: MassDensityUnit[1];
}
attribute massDensity: MassDensityValue[*] nonunique :> scalarQuantities;
attribute def MassDensityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -3; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF); }
}
alias DensityUnit for MassDensityUnit;
alias DensityValue for MassDensityValue;
alias density for massDensity;
/* ISO-80000-4 item 4-3 specific volume */
attribute def SpecificVolumeValue :> ScalarQuantityValue {
doc
/*
* source: item 4-3 specific volume
* symbol(s): `v`
* application domain: generic
* name: SpecificVolume
* quantity dimension: L^3*M^-1
* measurement unit(s): kg^-1*m^3
* tensor order: 0
* definition: reciprocal of mass density `ρ` (item 4-2): `v = 1/ρ`
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: SpecificVolumeUnit[1];
}
attribute specificVolume: SpecificVolumeValue[*] nonunique :> scalarQuantities;
attribute def SpecificVolumeUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 3; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF); }
}
/* ISO-80000-4 item 4-4 relative mass density, relative density */
attribute def RelativeMassDensityValue :> DimensionOneValue {
doc
/*
* source: item 4-4 relative mass density, relative density
* symbol(s): `d`
* application domain: generic
* name: RelativeMassDensity (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: quotient of mass density of a substance `ρ` and mass density of a reference substance `ρ_0` : `d = ρ/ρ_0`
* remarks: Conditions and material should be specified for the reference substance.
*/
}
attribute relativeMassDensity: RelativeMassDensityValue :> scalarQuantities;
alias relativeDensity for relativeMassDensity;
/* ISO-80000-4 item 4-5 surface mass density, surface density */
attribute def SurfaceMassDensityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-5 surface mass density, surface density
* symbol(s): `ρ_A`
* application domain: generic
* name: SurfaceMassDensity
* quantity dimension: L^-2*M^1
* measurement unit(s): kg*m^-2
* tensor order: 0
* definition: quantity representing the areal distribution of mass of a continuous material: `ρ_A(vec(r)) = (dm)/(dA)` where `m` is the mass of the material at position `vec(r)` and `A` is area
* remarks: The name "grammage" should not be used for this quantity.
*/
attribute :>> num: Real;
attribute :>> mRef: SurfaceMassDensityUnit[1];
}
attribute surfaceMassDensity: SurfaceMassDensityValue[*] nonunique :> scalarQuantities;
attribute def SurfaceMassDensityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF); }
}
alias SurfaceDensityUnit for SurfaceMassDensityUnit;
alias SurfaceDensityValue for SurfaceMassDensityValue;
alias surfaceDensity for surfaceMassDensity;
/* ISO-80000-4 item 4-6 linear mass density, linear density */
attribute def LinearMassDensityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-6 linear mass density, linear density
* symbol(s): `ρ_I`
* application domain: generic
* name: LinearMassDensity
* quantity dimension: L^-1*M^1
* measurement unit(s): kg*m^-1
* tensor order: 0
* definition: quantity representing the linear distribution of mass of a continuous material: `ρ_I(vec(r)) = (dm)/(dI)` where `m` is the mass of the material at position `vec(r)` and `l` is length
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: LinearMassDensityUnit[1];
}
attribute linearMassDensity: LinearMassDensityValue[*] nonunique :> scalarQuantities;
attribute def LinearMassDensityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF); }
}
alias LinearDensityUnit for LinearMassDensityUnit;
alias LinearDensityValue for LinearMassDensityValue;
alias linearDensity for linearMassDensity;
/* ISO-80000-4 item 4-7 moment of inertia */
attribute def MomentOfInertiaValue :> ScalarQuantityValue {
doc
/*
* source: item 4-7 moment of inertia (magnitude)
* symbol(s): `J`
* application domain: generic
* name: MomentOfInertia
* quantity dimension: L^2*M^1
* measurement unit(s): kg*m^2
* tensor order: 0
* definition: tensor (ISO 80000-2) quantity representing rotational inertia of a rigid body relative to a fixed centre of rotation expressed by the tensor product: `vec(L) = vec(vec(J)) vec(ω)` where `vec(L)` is angular momentum (item 4-11) of the body relative to the reference point and `vec(ω)` is its angular velocity (ISO 80000-3)
* remarks: The calculation of the value requires an integration.
*/
attribute :>> num: Real;
attribute :>> mRef: MomentOfInertiaUnit[1];
}
attribute momentOfInertia: MomentOfInertiaValue[*] nonunique :> scalarQuantities;
attribute def MomentOfInertiaUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF); }
}
attribute def Cartesian3dMomentOfInertiaTensor :> TensorQuantityValue {
doc
/*
* source: item 4-7 moment of inertia (tensor)
* symbol(s): `vec(vec(J))`
* application domain: generic
* name: MomentOfInertia
* quantity dimension: L^2*M^1
* measurement unit(s): kg*m^2
* tensor order: 2
* definition: tensor (ISO 80000-2) quantity representing rotational inertia of a rigid body relative to a fixed centre of rotation expressed by the tensor product: `vec(L) = vec(vec(J)) vec(ω)` where `vec(L)` is angular momentum (item 4-11) of the body relative to the reference point and `vec(ω)` is its angular velocity (ISO 80000-3)
* remarks: The calculation of the value requires an integration.
*/
attribute :>> isBound = false;
attribute :>> num: Real[9];
attribute :>> mRef: Cartesian3dMomentOfInertiaMeasurementReference[1];
}
attribute momentOfInertiaTensor: Cartesian3dMomentOfInertiaTensor :> tensorQuantities;
attribute def Cartesian3dMomentOfInertiaMeasurementReference :> TensorMeasurementReference {
attribute :>> dimensions = (3, 3);
attribute :>> isBound = false;
attribute :>> mRefs: MomentOfInertiaUnit[9];
}
/* ISO-80000-4 item 4-8 momentum */
attribute def MomentumValue :> ScalarQuantityValue {
doc
/*
* source: item 4-8 momentum (magnitude)
* symbol(s): `p`
* application domain: generic
* name: Momentum
* quantity dimension: L^1*M^1*T^-1
* measurement unit(s): kg*m*s^-1
* tensor order: 0
* definition: product of mass `m` (item 4-1) of a body and velocity `vec(v)` (ISO 80000-3) of its centre of mass: `vec(p) = m vec(v)`
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: MomentumUnit[1];
}
attribute momentum: MomentumValue[*] nonunique :> scalarQuantities;
attribute def MomentumUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
attribute def Cartesian3dMomentumVector :> VectorQuantityValue {
doc
/*
* source: item 4-8 momentum (vector)
* symbol(s): `vec(p)`
* application domain: generic
* name: Momentum
* quantity dimension: L^1*M^1*T^-1
* measurement unit(s): kg*m*s^-1
* tensor order: 1
* definition: product of mass `m` (item 4-1) of a body and velocity `vec(v)` (ISO 80000-3) of its centre of mass: `vec(p) = m vec(v)`
* remarks: None.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dMomentumCoordinateFrame[1];
}
attribute momentumVector: Cartesian3dMomentumVector :> vectorQuantities;
attribute def Cartesian3dMomentumCoordinateFrame :> VectorMeasurementReference {
attribute :>> dimensions = 3;
attribute :>> isBound = false;
attribute :>> isOrthogonal = true;
attribute :>> mRefs: MomentumUnit[3];
}
/* ISO-80000-4 item 4-9.1 force */
attribute def ForceValue :> ScalarQuantityValue {
doc
/*
* source: item 4-9.1 force (magnitude)
* symbol(s): `F`
* application domain: generic
* name: Force
* quantity dimension: L^1*M^1*T^-2
* measurement unit(s): N, kg*m*s^-2
* tensor order: 0
* definition: vector (ISO 80000-2) quantity describing interaction between bodies or particles
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: ForceUnit[1];
}
attribute force: ForceValue[*] nonunique :> scalarQuantities;
attribute def ForceUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
attribute def Cartesian3dForceVector :> VectorQuantityValue {
doc
/*
* source: item 4-9.1 force (vector)
* symbol(s): `vec(F)`
* application domain: generic
* name: Force
* quantity dimension: L^1*M^1*T^-2
* measurement unit(s): N, kg*m*s^-2
* tensor order: 1
* definition: vector (ISO 80000-2) quantity describing interaction between bodies or particles
* remarks: None.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dForceCoordinateFrame[1];
}
attribute forceVector: Cartesian3dForceVector :> vectorQuantities;
attribute def Cartesian3dForceCoordinateFrame :> VectorMeasurementReference {
attribute :>> dimensions = 3;
attribute :>> isBound = false;
attribute :>> isOrthogonal = true;
attribute :>> mRefs: ForceUnit[3];
}
/* ISO-80000-4 item 4-9.2 weight */
attribute def Cartesian3dWeightVector :> VectorQuantityValue {
doc
/*
* source: item 4-9.2 weight
* symbol(s): `vec(F_g)`
* application domain: generic
* name: Weight (specializes Force)
* quantity dimension: L^1*M^1*T^-2
* measurement unit(s): N, kg*m*s^-2
* tensor order: 1
* definition: force (item 4-9.1) acting on a body in the gravitational field of Earth: `vec(F_g) = m vec(g)` where `m` (item 4-1) is the mass of the body and `vec(g)` is the local acceleration of free fall (ISO 80000-3)
* remarks: In colloquial language, the name "weight" continues to be used where "mass" is meant. This practice should be avoided. Weight is an example of a gravitational force. Weight comprises not only the local gravitational force but also the local centrifugal force due to the rotation of the Earth.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dForceCoordinateFrame[1];
}
attribute weightVector: Cartesian3dWeightVector :> vectorQuantities;
/* ISO-80000-4 item 4-9.3 static friction force, static friction */
attribute def Cartesian3dStaticFrictionForceVector :> VectorQuantityValue {
doc
/*
* source: item 4-9.3 static friction force, static friction
* symbol(s): `vec(F_s)`
* application domain: generic
* name: StaticFrictionForce (specializes Force)
* quantity dimension: L^1*M^1*T^-2
* measurement unit(s): N, kg*m*s^-2
* tensor order: 1
* definition: force (item 4-9.1) resisting the motion before a body starts to slide on a surface
* remarks: For the static friction coefficient, see item 4-23.1.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dForceCoordinateFrame[1];
}
attribute staticFrictionForceVector: Cartesian3dStaticFrictionForceVector :> vectorQuantities;
alias staticFrictionVector for staticFrictionForceVector;
/* ISO-80000-4 item 4-9.4 kinetic friction force, dynamic friction force */
attribute def Cartesian3dKineticFrictionForceVector :> VectorQuantityValue {
doc
/*
* source: item 4-9.4 kinetic friction force, dynamic friction force
* symbol(s): `vec(F_μ)`
* application domain: generic
* name: KineticFrictionForce (specializes Force)
* quantity dimension: L^1*M^1*T^-2
* measurement unit(s): N, kg*m*s^-2
* tensor order: 1
* definition: force (item 4-9.1) resisting the motion when a body slides on a surface
* remarks: For the kinetic friction factor, see item 4-23.2.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dForceCoordinateFrame[1];
}
attribute kineticFrictionForceVector: Cartesian3dKineticFrictionForceVector :> vectorQuantities;
alias dynamicFrictionForceVector for kineticFrictionForceVector;
/* ISO-80000-4 item 4-9.5 rolling resistance, rolling drag, rolling friction force */
attribute def Cartesian3dRollingResistanceVector :> VectorQuantityValue {
doc
/*
* source: item 4-9.5 rolling resistance, rolling drag, rolling friction force
* symbol(s): `vec(F_"rr")`
* application domain: generic
* name: RollingResistance (specializes Force)
* quantity dimension: L^1*M^1*T^-2
* measurement unit(s): N, kg*m*s^-2
* tensor order: 1
* definition: force (item 4-9.1) resisting the motion when a body rolls on a surface
* remarks: For the rolling resistance factor, see item 4-23.3.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dForceCoordinateFrame[1];
}
attribute rollingResistanceVector: Cartesian3dRollingResistanceVector :> vectorQuantities;
alias rollingDragVector for rollingResistanceVector;
alias rollingFrictionForceVector for rollingResistanceVector;
/* ISO-80000-4 item 4-9.6 drag force */
attribute def Cartesian3dDragForceVector :> VectorQuantityValue {
doc
/*
* source: item 4-9.6 drag force
* symbol(s): `vec(F_D)`
* application domain: generic
* name: DragForce (specializes Force)
* quantity dimension: L^1*M^1*T^-2
* measurement unit(s): N, kg*m*s^-2
* tensor order: 1
* definition: force (item 4-9.1) resisting the motion of a body in a fluid
* remarks: For the drag coefficient, see item 4-23.4.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dForceCoordinateFrame[1];
}
attribute dragForceVector: Cartesian3dDragForceVector :> vectorQuantities;
/* ISO-80000-4 item 4-10 impulse */
attribute def ImpulseValue :> ScalarQuantityValue {
doc
/*
* source: item 4-10 impulse (magnitude)
* symbol(s): `I`
* application domain: generic
* name: Impulse
* quantity dimension: L^1*M^1*T^-1
* measurement unit(s): N*s, kg*m*s^-1
* tensor order: 0
* definition: vector (ISO 80000-2) quantity describing the effect of force acting during a time interval: `vec(I) = int_(t_1)^(t_2) vec(F)*dt` where `vec(F)` is force (item 4-9.1), `t` is time (ISO 80000-3) and `[t_1, t_2]` is considered time interval
* remarks: For a time interval `[t_1, t_2]`, `vec(I)(t_1, t_2) = vec(p)(t_1) - vec(p)(t_2) = vec(Δp)` where `vec(p)` is momentum (item 4-8).
*/
attribute :>> num: Real;
attribute :>> mRef: ImpulseUnit[1];
}
attribute impulse: ImpulseValue[*] nonunique :> scalarQuantities;
attribute def ImpulseUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
attribute def Cartesian3dImpulseVector :> VectorQuantityValue {
doc
/*
* source: item 4-10 impulse (vector)
* symbol(s): `vec(I)`
* application domain: generic
* name: Impulse
* quantity dimension: L^1*M^1*T^-1
* measurement unit(s): N*s, kg*m*s^-1
* tensor order: 1
* definition: vector (ISO 80000-2) quantity describing the effect of force acting during a time interval: `vec(I) = int_(t_1)^(t_2) vec(F)*dt` where `vec(F)` is force (item 4-9.1), `t` is time (ISO 80000-3) and `[t_1, t_2]` is considered time interval
* remarks: For a time interval `[t_1, t_2]`, `vec(I)(t_1, t_2) = vec(p)(t_1) - vec(p)(t_2) = vec(Δp)` where `vec(p)` is momentum (item 4-8).
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dImpulseCoordinateFrame[1];
}
attribute impulseVector: Cartesian3dImpulseVector :> vectorQuantities;
attribute def Cartesian3dImpulseCoordinateFrame :> VectorMeasurementReference {
attribute :>> dimensions = 3;
attribute :>> isBound = false;
attribute :>> isOrthogonal = true;
attribute :>> mRefs: ImpulseUnit[3];
}
/* ISO-80000-4 item 4-11 angular momentum */
attribute def AngularMomentumValue :> ScalarQuantityValue {
doc
/*
* source: item 4-11 angular momentum (magnitude)
* symbol(s): `L`
* application domain: generic
* name: AngularMomentum
* quantity dimension: L^2*M^1*T^-1
* measurement unit(s): kg*m^2*s^-1
* tensor order: 0
* definition: vector (ISO 80000-2) quantity described by the vector product: `vec(L) = vec(r) xx vec(p)` where `vec(r)` is position vector (ISO 80000-3) with respect to the axis of rotation and `vec(p)` is momentum (item 4-8)
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: AngularMomentumUnit[1];
}
attribute angularMomentum: AngularMomentumValue[*] nonunique :> scalarQuantities;
attribute def AngularMomentumUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
attribute def Cartesian3dAngularMomentumVector :> VectorQuantityValue {
doc
/*
* source: item 4-11 angular momentum (vector)
* symbol(s): `vec(L)`
* application domain: generic
* name: AngularMomentum
* quantity dimension: L^2*M^1*T^-1
* measurement unit(s): kg*m^2*s^-1
* tensor order: 1
* definition: vector (ISO 80000-2) quantity described by the vector product: `vec(L) = vec(r) xx vec(p)` where `vec(r)` is position vector (ISO 80000-3) with respect to the axis of rotation and `vec(p)` is momentum (item 4-8)
* remarks: None.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dAngularMomentumCoordinateFrame[1];
}
attribute angularMomentumVector: Cartesian3dAngularMomentumVector :> vectorQuantities;
attribute def Cartesian3dAngularMomentumCoordinateFrame :> VectorMeasurementReference {
attribute :>> dimensions = 3;
attribute :>> isBound = false;
attribute :>> isOrthogonal = true;
attribute :>> mRefs: AngularMomentumUnit[3];
}
/* ISO-80000-4 item 4-12.1 moment of force */
attribute def MomentOfForceValue :> ScalarQuantityValue {
doc
/*
* source: item 4-12.1 moment of force (magnitude)
* symbol(s): `M`
* application domain: generic
* name: MomentOfForce
* quantity dimension: L^2*M^1*T^-2
* measurement unit(s): N*m, kg*m^2*s^-2
* tensor order: 0
* definition: vector (ISO 80000-2) quantity described by the vector product: `vec(M) = vec(r) xx vec(F)` where `vec(r)` is position vector (ISO 80000-3) with respect to the axis of rotation and `vec(F)` is force (item 4-9.1)
* remarks: The bending moment of force is denoted by `vec(M)_b`.
*/
attribute :>> num: Real;
attribute :>> mRef: MomentOfForceUnit[1];
}
attribute momentOfForce: MomentOfForceValue[*] nonunique :> scalarQuantities;
attribute def MomentOfForceUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
attribute def Cartesian3dMomentOfForceVector :> VectorQuantityValue {
doc
/*
* source: item 4-12.1 moment of force (vector)
* symbol(s): `vec(M)`
* application domain: generic
* name: MomentOfForce
* quantity dimension: L^2*M^1*T^-2
* measurement unit(s): N*m, kg*m^2*s^-2
* tensor order: 1
* definition: vector (ISO 80000-2) quantity described by the vector product: `vec(M) = vec(r) xx vec(F)` where `vec(r)` is position vector (ISO 80000-3) with respect to the axis of rotation and `vec(F)` is force (item 4-9.1)
* remarks: The bending moment of force is denoted by `vec(M)_b`.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dMomentOfForceCoordinateFrame[1];
}
attribute momentOfForceVector: Cartesian3dMomentOfForceVector :> vectorQuantities;
attribute def Cartesian3dMomentOfForceCoordinateFrame :> VectorMeasurementReference {
attribute :>> dimensions = 3;
attribute :>> isBound = false;
attribute :>> isOrthogonal = true;
attribute :>> mRefs: MomentOfForceUnit[3];
}
/* ISO-80000-4 item 4-12.2 torque */
attribute def TorqueValue :> ScalarQuantityValue {
doc
/*
* source: item 4-12.2 torque
* symbol(s): `T`, `M_Q`
* application domain: generic
* name: Torque
* quantity dimension: L^2*M^1*T^-2
* measurement unit(s): N*m, kg*m^2*s^-2
* tensor order: 0
* definition: quantity described by the scalar product: `T = vec(M)*vec(e_Q)` where `vec(M)` is moment of force (item 4-12.1) and `vec(e_Q)` is unit vector of direction with respect to which the torque is considered
* remarks: For example, torque is the twisting moment of force with respect to the longitudinal axis of a beam or shaft.
*/
attribute :>> num: Real;
attribute :>> mRef: TorqueUnit[1];
}
attribute torque: TorqueValue[*] nonunique :> scalarQuantities;
attribute def TorqueUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
/* ISO-80000-4 item 4-13 angular impulse */
attribute def AngularImpulseValue :> ScalarQuantityValue {
doc
/*
* source: item 4-13 angular impulse (magnitude)
* symbol(s): `H`
* application domain: generic
* name: AngularImpulse
* quantity dimension: L^2*M^1*T^-1
* measurement unit(s): N*m*s, kg*m^2*s^-1
* tensor order: 0
* definition: vector (ISO 80000-2) quantity describing the effect of moment of force during a time interval: `vec(H)(t_1; t_2) = int_(t_1)^(t_2) vec(M) dt` where `vec(M)` is moment of force (item 4-12.1), `t` is time (ISO 80000-3) and `[t_1, t_2]` is considered time interval
* remarks: For a time interval `[t_1, t_2]`, `vec(H)(t_1, t_2) = vec(L)(t_1) - vec(L)(t_2) = vec(ΔL)` where `vec(L)` is angular momentum.
*/
attribute :>> num: Real;
attribute :>> mRef: AngularImpulseUnit[1];
}
attribute angularImpulse: AngularImpulseValue[*] nonunique :> scalarQuantities;
attribute def AngularImpulseUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
attribute def Cartesian3dAngularImpulseVector :> VectorQuantityValue {
doc
/*
* source: item 4-13 angular impulse (vector)
* symbol(s): `vec(H)`
* application domain: generic
* name: AngularImpulse
* quantity dimension: L^2*M^1*T^-1
* measurement unit(s): N*m*s, kg*m^2*s^-1
* tensor order: 1
* definition: vector (ISO 80000-2) quantity describing the effect of moment of force during a time interval: `vec(H)(t_1; t_2) = int_(t_1)^(t_2) vec(M) dt` where `vec(M)` is moment of force (item 4-12.1), `t` is time (ISO 80000-3) and `[t_1, t_2]` is considered time interval
* remarks: For a time interval `[t_1, t_2]`, `vec(H)(t_1, t_2) = vec(L)(t_1) - vec(L)(t_2) = vec(ΔL)` where `vec(L)` is angular momentum.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dAngularImpulseCoordinateFrame[1];
}
attribute angularImpulseVector: Cartesian3dAngularImpulseVector :> vectorQuantities;
attribute def Cartesian3dAngularImpulseCoordinateFrame :> VectorMeasurementReference {
attribute :>> dimensions = 3;
attribute :>> isBound = false;
attribute :>> isOrthogonal = true;
attribute :>> mRefs: AngularImpulseUnit[3];
}
/* ISO-80000-4 item 4-14.1 pressure */
attribute def PressureValue :> ScalarQuantityValue {
doc
/*
* source: item 4-14.1 pressure
* symbol(s): `p`
* application domain: generic
* name: Pressure
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 0
* definition: quotient of the component of a force normal to a surface and its area: `p = (vec(e_n) * vec(F)) / A` where `vec(e_n)` is unit vector of the surface normal, `vec(F)` is force (item 4-9.1) and `A` is area (ISO 80000-3)
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: PressureUnit[1];
}
attribute pressure: PressureValue[*] nonunique :> scalarQuantities;
attribute def PressureUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
/* ISO-80000-4 item 4-14.2 gauge pressure */
attribute gaugePressure: PressureValue :> scalarQuantities {
doc
/*
* source: item 4-14.2 gauge pressure
* symbol(s): `p_e`
* application domain: generic
* name: GaugePressure (specializes Pressure)
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 0
* definition: pressure `p` (item 4-14.1) decremented by ambient pressure `p_amb` : `p_e = p - p_amb`
* remarks: Often, `p_amb` is chosen as a standard pressure. Gauge pressure is positive or negative.
*/
}
/* ISO-80000-4 item 4-15 stress */
attribute def StressValue :> ScalarQuantityValue {
doc
/*
* source: item 4-15 stress (magnitude)
* symbol(s): `σ`
* application domain: generic
* name: Stress
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 0
* definition: tensor (ISO 80000-2) quantity representing state of tension of matter
* remarks: Stress tensor is symmetric and has three normal-stress and three shear-stress (Cartesian) components.
*/
attribute :>> num: Real;
attribute :>> mRef: StressUnit[1];
}
attribute stress: StressValue[*] nonunique :> scalarQuantities;
attribute def StressUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
attribute def Cartesian3dStressTensor :> TensorQuantityValue {
doc
/*
* source: item 4-15 stress (tensor)
* symbol(s): `vec(vec(σ))`
* application domain: generic
* name: Stress
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 2
* definition: tensor (ISO 80000-2) quantity representing state of tension of matter
* remarks: Stress tensor is symmetric and has three normal-stress and three shear-stress (Cartesian) components.
*/
attribute :>> isBound = false;
attribute :>> num: Real[9];
attribute :>> mRef: Cartesian3dStressMeasurementReference[1];
}
attribute stressTensor: Cartesian3dStressTensor :> tensorQuantities;
attribute def Cartesian3dStressMeasurementReference :> TensorMeasurementReference {
attribute :>> dimensions = (3, 3);
attribute :>> isBound = false;
attribute :>> mRefs: StressUnit[9];
}
/* ISO-80000-4 item 4-16.1 normal stress */
attribute def NormalStressValue :> ScalarQuantityValue {
doc
/*
* source: item 4-16.1 normal stress
* symbol(s): `σ_n`, `σ`
* application domain: generic
* name: NormalStress
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 0
* definition: scalar (ISO 80000-2) quantity describing surface action of a force into a body equal to: `σ_n = (d F_n)/(dA)` where `F_n` is the normal component of force (item 4-9.1) and `A` is the area (ISO 80000-3) of the surface element
* remarks: A couple of mutually opposite forces of magnitude `F` acting on the opposite surfaces of a slice (layer) of homogenous solid matter normal to it, and evenly distributed, cause a constant normal stress `σ_n = F A` in the slice (layer).
*/
attribute :>> num: Real;
attribute :>> mRef: NormalStressUnit[1];
}
attribute normalStress: NormalStressValue[*] nonunique :> scalarQuantities;
attribute def NormalStressUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
/* ISO-80000-4 item 4-16.2 shear stress */
attribute def ShearStressValue :> ScalarQuantityValue {
doc
/*
* source: item 4-16.2 shear stress
* symbol(s): `τ_s`, `τ`
* application domain: generic
* name: ShearStress
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 0
* definition: scalar (ISO 80000-2) quantity describing surface action of a force into a body equal to: `τ_s = (d F_t)/(dA)` where `F_t` is the tangential component of force (item 4-9.1) and `A` is the area (ISO 80000-3) of the surface element
* remarks: A couple of mutually opposite forces of magnitude `F` acting on the opposite surfaces of a slice (layer) of homogenous solid matter parallel to it, and evenly distributed, cause a constant shear stress `τ = F/A` in the slice (layer).
*/
attribute :>> num: Real;
attribute :>> mRef: ShearStressUnit[1];
}
attribute shearStress: ShearStressValue[*] nonunique :> scalarQuantities;
attribute def ShearStressUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
/* ISO-80000-4 item 4-17.1 strain */
attribute def StrainValue :> ScalarQuantityValue {
doc
/*
* source: item 4-17.1 strain (magnitude)
* symbol(s): `ε`
* application domain: generic
* name: Strain
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: tensor (ISO 80000-2) quantity representing the deformation of matter caused by stress
* remarks: Strain tensor is symmetric and has three linear-strain and three shear strain (Cartesian) components.
*/
attribute :>> num: Real;
attribute :>> mRef: StrainUnit[1];
}
attribute strain: StrainValue[*] nonunique :> scalarQuantities;
attribute def StrainUnit :> DimensionOneUnit {
}
attribute def Cartesian3dStrainTensor :> TensorQuantityValue {
doc
/*
* source: item 4-17.1 strain (tensor)
* symbol(s): `vec(vec(ε))`
* application domain: generic
* name: Strain
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 2
* definition: tensor (ISO 80000-2) quantity representing the deformation of matter caused by stress
* remarks: Strain tensor is symmetric and has three linear-strain and three shear strain (Cartesian) components.
*/
attribute :>> isBound = false;
attribute :>> num: Real[9];
attribute :>> mRef: Cartesian3dStrainMeasurementReference[1];
}
attribute strainTensor: Cartesian3dStrainTensor :> tensorQuantities;
attribute def Cartesian3dStrainMeasurementReference :> TensorMeasurementReference {
attribute :>> dimensions = (3, 3);
attribute :>> isBound = false;
attribute :>> mRefs: StrainUnit[9];
}
/* ISO-80000-4 item 4-17.2 relative linear strain */
attribute def RelativeLinearStrainValue :> DimensionOneValue {
doc
/*
* source: item 4-17.2 relative linear strain
* symbol(s): `ε`, `(e)`
* application domain: generic
* name: RelativeLinearStrain (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: quotient of change in length `Δl` (ISO 80000-3) of an object and its length `l` (ISO 80000-3): `ε = (Δl)/l`
* remarks: None.
*/
}
attribute relativeLinearStrain: RelativeLinearStrainValue :> scalarQuantities;
/* ISO-80000-4 item 4-17.3 shear strain */
attribute def ShearStrainValue :> DimensionOneValue {
doc
/*
* source: item 4-17.3 shear strain
* symbol(s): `γ`
* application domain: generic
* name: ShearStrain (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: quotient of parallel displacement `Δx` (ISO 80000-3) of two surfaces of a layer and the thickness `d` (ISO 80000-3) of the layer: `γ = (Δx)/d`
* remarks: None.
*/
}
attribute shearStrain: ShearStrainValue :> scalarQuantities;
/* ISO-80000-4 item 4-17.4 relative volume strain */
attribute def RelativeVolumeStrainValue :> DimensionOneValue {
doc
/*
* source: item 4-17.4 relative volume strain
* symbol(s): `θ`
* application domain: generic
* name: RelativeVolumeStrain (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: quotient of change in volume `ΔV` (ISO 80000-3) of an object and its volume `V_0` (ISO 80000-3): `θ = (ΔV)/V_0`
* remarks: None.
*/
}
attribute relativeVolumeStrain: RelativeVolumeStrainValue :> scalarQuantities;
/* ISO-80000-4 item 4-18 Poisson number */
attribute def PoissonNumberValue :> DimensionOneValue {
doc
/*
* source: item 4-18 Poisson number
* symbol(s): `μ`, `(v)`
* application domain: generic
* name: PoissonNumber (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: quotient of change in width `Δb` (width is defined in ISO 80000-3) and change in length `Δl` (length is defined in ISO 80000-3) of an object: `μ = (Δb)/(Δl)`
* remarks: None.
*/
}
attribute poissonNumber: PoissonNumberValue :> scalarQuantities;
/* ISO-80000-4 item 4-19.1 modulus of elasticity, Young modulus */
attribute def ModulusOfElasticityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-19.1 modulus of elasticity, Young modulus
* symbol(s): `E`, `E_m`, `Y`
* application domain: generic
* name: ModulusOfElasticity
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 0
* definition: quotient of normal stress `σ` (item 4-16.1) and relative linear strain `ε` (item 4-17.2): `E = σ/ε`
* remarks: Conditions should be specified (e.g. adiabatic or isothermal process).
*/
attribute :>> num: Real;
attribute :>> mRef: ModulusOfElasticityUnit[1];
}
attribute modulusOfElasticity: ModulusOfElasticityValue[*] nonunique :> scalarQuantities;
attribute def ModulusOfElasticityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
alias YoungModulusUnit for ModulusOfElasticityUnit;
alias YoungModulusValue for ModulusOfElasticityValue;
alias youngModulus for modulusOfElasticity;
/* ISO-80000-4 item 4-19.2 modulus of rigidity, shear modulus */
attribute def ModulusOfRigidityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-19.2 modulus of rigidity, shear modulus
* symbol(s): `G`
* application domain: generic
* name: ModulusOfRigidity
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 0
* definition: quotient of shear stress `τ` (item 4-16.2) and shear strain `γ` (item 4-17.3): `G = τ/γ`
* remarks: Conditions should be specified (e.g. isentropic or isothermal process).
*/
attribute :>> num: Real;
attribute :>> mRef: ModulusOfRigidityUnit[1];
}
attribute modulusOfRigidity: ModulusOfRigidityValue[*] nonunique :> scalarQuantities;
attribute def ModulusOfRigidityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
alias ShearModulusUnit for ModulusOfRigidityUnit;
alias ShearModulusValue for ModulusOfRigidityValue;
alias shearModulus for modulusOfRigidity;
/* ISO-80000-4 item 4-19.3 modulus of compression, bulk modulus */
attribute def ModulusOfCompressionValue :> ScalarQuantityValue {
doc
/*
* source: item 4-19.3 modulus of compression, bulk modulus
* symbol(s): `K`, `K_m`, `B`
* application domain: generic
* name: ModulusOfCompression
* quantity dimension: L^-1*M^1*T^-2
* measurement unit(s): Pa, N*m^-2, kg*m^-1*s^-2
* tensor order: 0
* definition: negative of the quotient of pressure `p` (item 4-14.1) and relative volume strain `θ` (item 4-17.4): `K = -(p/θ)`
* remarks: Conditions should be specified (e.g. isentropic or isothermal process).
*/
attribute :>> num: Real;
attribute :>> mRef: ModulusOfCompressionUnit[1];
}
attribute modulusOfCompression: ModulusOfCompressionValue[*] nonunique :> scalarQuantities;
attribute def ModulusOfCompressionUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
alias BulkModulusUnit for ModulusOfCompressionUnit;
alias BulkModulusValue for ModulusOfCompressionValue;
alias bulkModulus for modulusOfCompression;
/* ISO-80000-4 item 4-20 compressibility */
attribute def CompressibilityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-20 compressibility
* symbol(s): `ϰ`
* application domain: generic
* name: Compressibility
* quantity dimension: L^1*M^-1*T^2
* measurement unit(s): Pa^-1, kg^-1*m*s^2
* tensor order: 0
* definition: negative relative change of volume `V` (ISO 80000-3) of an object under pressure `p` (item 4-14.1) expressed by: `ϰ = -(1/V)(dV)/(dp)`
* remarks: Conditions should be specified (e.g. isentropic or isothermal process). See also ISO 80000-5.
*/
attribute :>> num: Real;
attribute :>> mRef: CompressibilityUnit[1];
}
attribute compressibility: CompressibilityValue[*] nonunique :> scalarQuantities;
attribute def CompressibilityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = -1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = 2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
/* ISO-80000-4 item 4-21.1 second axial moment of area */
attribute def SecondAxialMomentOfAreaValue :> ScalarQuantityValue {
doc
/*
* source: item 4-21.1 second axial moment of area
* symbol(s): `I_a`
* application domain: generic
* name: SecondAxialMomentOfArea
* quantity dimension: L^4
* measurement unit(s): m^4
* tensor order: 0
* definition: geometrical characteristic of a shape of a body equal to: `I_a = int int_M r_Q^2 dA` where `M` is the two-dimensional domain of the cross-section of a plane and considered body, `r_Q` is radial distance (ISO 80000-3) from a Q-axis in the plane of the surface considered and `A` is area (ISO 80000-3)
* remarks: This quantity is often referred to wrongly as "moment of inertia" (item 4-7). The subscript, `a`, may be omitted when there is no risk of confusion.
*/
attribute :>> num: Real;
attribute :>> mRef: SecondAxialMomentOfAreaUnit[1];
}
attribute secondAxialMomentOfArea: SecondAxialMomentOfAreaValue[*] nonunique :> scalarQuantities;
attribute def SecondAxialMomentOfAreaUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 4; }
attribute :>> quantityDimension { :>> quantityPowerFactors = lengthPF; }
}
/* ISO-80000-4 item 4-21.2 second polar moment of area */
attribute def SecondPolarMomentOfAreaValue :> ScalarQuantityValue {
doc
/*
* source: item 4-21.2 second polar moment of area
* symbol(s): `I_p`
* application domain: generic
* name: SecondPolarMomentOfArea
* quantity dimension: L^4
* measurement unit(s): m^4
* tensor order: 0
* definition: geometrical characteristic of a shape of a body equal to: `I_p = int int_M r_Q^2 * dA` where `M` is the two-dimensional domain of the cross-section of a plane and considered body, `r_Q` is radial distance (ISO 80000-3) from a Q-axis perpendicular to the plane of the surface considered and `A` is area (ISO 80000-3)
* remarks: This quantity is often referred to wrongly as "moment of inertia" (item 4-7). The subscript, `p`, may be omitted when there is no risk of confusion.
*/
attribute :>> num: Real;
attribute :>> mRef: SecondPolarMomentOfAreaUnit[1];
}
attribute secondPolarMomentOfArea: SecondPolarMomentOfAreaValue[*] nonunique :> scalarQuantities;
attribute def SecondPolarMomentOfAreaUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 4; }
attribute :>> quantityDimension { :>> quantityPowerFactors = lengthPF; }
}
/* ISO-80000-4 item 4-22 section modulus */
attribute def SectionModulusValue :> ScalarQuantityValue {
doc
/*
* source: item 4-22 section modulus
* symbol(s): `Z`, `(W)`
* application domain: generic
* name: SectionModulus
* quantity dimension: L^3
* measurement unit(s): m^3
* tensor order: 0
* definition: geometrical characteristic of a shape of a body equal to: `Z = I_a/r_(Q_max)` where `I_a` is the second axial moment of area (item 4-21.1) and `r_(Q,max)` is the maximum radial distance (ISO 80000-3) of any point in the surface considered from the Q-axis with respect to which `I_a` is defined
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: SectionModulusUnit[1];
}
attribute sectionModulus: SectionModulusValue[*] nonunique :> scalarQuantities;
attribute def SectionModulusUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 3; }
attribute :>> quantityDimension { :>> quantityPowerFactors = lengthPF; }
}
/* ISO-80000-4 item 4-23.1 static friction coefficient, static friction factor, coefficient of static friction */
attribute def StaticFrictionCoefficientValue :> DimensionOneValue {
doc
/*
* source: item 4-23.1 static friction coefficient, static friction factor, coefficient of static friction
* symbol(s): `μ_s`, `(f_s)`
* application domain: generic
* name: StaticFrictionCoefficient (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: proportionality factor between the maximum magnitude of the tangential component `F_max` of the static friction force (item 4-9.3) and the magnitude of the normal component `N` of the contact force (item 4-9.1) between two bodies at relative rest with respect to each other: `F_max = μ_s * N`
* remarks: When it is not necessary to distinguish between dynamic friction factor and static friction factor, the name friction factor may be used for both.
*/
}
attribute staticFrictionCoefficient: StaticFrictionCoefficientValue :> scalarQuantities;
alias staticFrictionFactor for staticFrictionCoefficient;
alias coefficientOfStaticFriction for staticFrictionCoefficient;
/* ISO-80000-4 item 4-23.2 kinetic friction factor, dynamic friction factor */
attribute def KineticFrictionFactorValue :> DimensionOneValue {
doc
/*
* source: item 4-23.2 kinetic friction factor, dynamic friction factor
* symbol(s): `μ`, `(f)`
* application domain: generic
* name: KineticFrictionFactor (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: proportionality factor between the magnitudes of the kinetic friction force, `F_μ` (item 4-9.4) and the normal component `N` of the contact force (item 4-9.1): `F_μ = μ * N`
* remarks: When it is not necessary to distinguish between dynamic friction factor and static friction factor, the name friction factor may be used for both. The dynamic friction factor `µ` is independent in first approximation of the contact surface.
*/
}
attribute kineticFrictionFactor: KineticFrictionFactorValue :> scalarQuantities;
alias dynamicFrictionFactor for kineticFrictionFactor;
/* ISO-80000-4 item 4-23.3 rolling resistance factor */
attribute def RollingResistanceFactorValue :> DimensionOneValue {
doc
/*
* source: item 4-23.3 rolling resistance factor
* symbol(s): `C_"rr"`
* application domain: generic
* name: RollingResistanceFactor (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: proportionality factor between the magnitude of the tangential component `F` and the magnitude of the normal component `N` of the force applied to a body rolling on a surface at constant speed: `F = C_(rr)*N`
* remarks: Also known as rolling resistance coefficient, RRC.
*/
}
attribute rollingResistanceFactor: RollingResistanceFactorValue :> scalarQuantities;
/* ISO-80000-4 item 4-23.4 drag coefficient, drag factor */
attribute def DragCoefficientValue :> DimensionOneValue {
doc
/*
* source: item 4-23.4 drag coefficient, drag factor
* symbol(s): `C_D`
* application domain: generic
* name: DragCoefficient (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: factor proportional to magnitude `F_D` of the drag force (item 4-9.6) of a body moving in a fluid, dependent on the shape and speed `v` (ISO 80000-3) of a body: `F_D = 1/2 * C_D * ρ * v^2 * A` where `ρ` is mass density (item 4-2) of the fluid and `A` is cross-section area (ISO 80000-3) of the body
* remarks: None.
*/
}
attribute dragCoefficient: DragCoefficientValue :> scalarQuantities;
alias dragFactor for dragCoefficient;
/* ISO-80000-4 item 4-24 dynamic viscosity, viscosity */
attribute def DynamicViscosityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-24 dynamic viscosity, viscosity
* symbol(s): `η`
* application domain: generic
* name: DynamicViscosity
* quantity dimension: L^-1*M^1*T^-1
* measurement unit(s): Pa*s, kg*m^-1*s^-1
* tensor order: 0
* definition: for laminar flows, proportionality constant between shear stress `τ_(xz)` (item 4-16.2) in a fluid moving with a velocity `v_x` (ISO 80000-3) and gradient `(d v_x)/dz` perpendicular to the plane of shear: `τ_(xz) = η (d v_x)/(dz)`
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: DynamicViscosityUnit[1];
}
attribute dynamicViscosity: DynamicViscosityValue[*] nonunique :> scalarQuantities;
attribute def DynamicViscosityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -1; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
alias ViscosityUnit for DynamicViscosityUnit;
alias ViscosityValue for DynamicViscosityValue;
alias viscosity for dynamicViscosity;
/* ISO-80000-4 item 4-25 kinematic viscosity */
attribute def KinematicViscosityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-25 kinematic viscosity
* symbol(s): `v`
* application domain: generic
* name: KinematicViscosity
* quantity dimension: L^2*T^-1
* measurement unit(s): m^2*s^-1
* tensor order: 0
* definition: quotient of dynamic viscosity `η` (item 4-24) and mass density `ρ` (item 4-2) of a fluid: `v = η/ρ`
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: KinematicViscosityUnit[1];
}
attribute kinematicViscosity: KinematicViscosityValue[*] nonunique :> scalarQuantities;
attribute def KinematicViscosityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 2; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, durationPF); }
}
/* ISO-80000-4 item 4-26 surface tension */
attribute def SurfaceTensionValue :> ScalarQuantityValue {
doc
/*
* source: item 4-26 surface tension
* symbol(s): `γ`, `σ`
* application domain: generic
* name: SurfaceTension
* quantity dimension: M^1*T^-2
* measurement unit(s): N*m^-1, kg*s^-2
* tensor order: 0
* definition: magnitude of a force acting against the enlargement of area portion of a surface separating a liquid from its surrounding
* remarks: The concept of surface energy is closely related to surface tension and has the same dimension.
*/
attribute :>> num: Real;
attribute :>> mRef: SurfaceTensionUnit[1];
}
attribute surfaceTension: SurfaceTensionValue[*] nonunique :> scalarQuantities;
attribute def SurfaceTensionUnit :> DerivedUnit {
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -2; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (massPF, durationPF); }
}
/* ISO-80000-4 item 4-27.1 power */
attribute def PowerValue :> ScalarQuantityValue {
doc
/*
* source: item 4-27.1 power
* symbol(s): `P`
* application domain: generic
* name: Power
* quantity dimension: L^2*M^1*T^-3
* measurement unit(s): W, J*s^-1, kg*m^2*s^-3
* tensor order: 0
* definition: quotient of energy (ISO 80000-5) and duration (ISO 80000-3)
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: PowerUnit[1];
}
attribute power: PowerValue[*] nonunique :> scalarQuantities;
attribute def PowerUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -3; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
/* ISO-80000-4 item 4-27 mechanical power */
attribute mechanicalPower: PowerValue :> scalarQuantities {
doc
/*
* source: item 4-27 mechanical power
* symbol(s): `P`
* application domain: mechanics
* name: MechanicalPower (specializes Power)
* quantity dimension: L^2*M^1*T^-3
* measurement unit(s): W, N*m*s^-1, kg*m^2*s^-3
* tensor order: 0
* definition: scalar product of force `vec(F)` (item 4-9.1) acting to a body and its velocity `vec(v)` (ISO 80000-3): `P = vec(F) * vec(v)`
* remarks: None.
*/
}
/* ISO-80000-4 item 4-28.1 potential energy */
attribute potentialEnergy: EnergyValue :> scalarQuantities {
doc
/*
* source: item 4-28.1 potential energy
* symbol(s): `V`, `E_p`
* application domain: generic
* name: PotentialEnergy (specializes Energy)
* quantity dimension: L^2*M^1*T^-2
* measurement unit(s): J, kg*m^2*s^-2
* tensor order: 0
* definition: for conservative force `vec(F)`, scalar additive quantity obeying condition `vec(F) = -nabla F`, if it exists
* remarks: For the definition of energy, see ISO 80000-5. A force is conservative when the force field is irrotational, i.e. `rot(F) = 0` , or `vec(F)` is perpendicular to the speed of the body to ensure `vec(F) * d vec(r) = 0` .
*/
}
/* ISO-80000-4 item 4-28.2 kinetic energy */
attribute kineticEnergy: EnergyValue :> scalarQuantities {
doc
/*
* source: item 4-28.2 kinetic energy
* symbol(s): `T`, `E_k`
* application domain: generic
* name: KineticEnergy (specializes Energy)
* quantity dimension: L^2*M^1*T^-2
* measurement unit(s): J, kg*m^2*s^-2
* tensor order: 0
* definition: scalar (ISO 80000-2) quantity characterizing a moving body expressed by: `T = 1/2 m v^2` where `m` is mass (item 4-1) of the body and `v` is its speed (ISO 80000-3)
* remarks: For the definition of energy, see ISO 80000-5.
*/
}
/* ISO-80000-4 item 4-28.3 mechanical energy */
attribute mechanicalEnergy: EnergyValue :> scalarQuantities {
doc
/*
* source: item 4-28.3 mechanical energy
* symbol(s): `E`, `W`
* application domain: generic
* name: MechanicalEnergy (specializes Energy)
* quantity dimension: L^2*M^1*T^-2
* measurement unit(s): J, kg*m^2*s^-2
* tensor order: 0
* definition: sum of kinetic energy `T` (item 4-28.2) and potential energy `V` (item 4-28.1): `E = T+V`
* remarks: The symbols `E` and `W` are also used for other kinds of energy. This definition is understood in a classical way and it does not include thermal motion.
*/
}
/* ISO-80000-4 item 4-28.4 mechanical work, work */
attribute mechanicalWork: EnergyValue :> scalarQuantities {
doc
/*
* source: item 4-28.4 mechanical work, work
* symbol(s): `A`, `W`
* application domain: generic
* name: MechanicalWork (specializes Energy)
* quantity dimension: L^2*M^1*T^-2
* measurement unit(s): J, kg*m^2*s^-2
* tensor order: 0
* definition: process quantity describing the total action of a force `vec(F)` (item 4-9.1) along a continuous curve `Γ` in three-dimensional space with infinitesimal displacement (ISO 80000-3) `dvec(r)`, as a line integral of their scalar product: `A = int_Γ vec(F) * d vec(r)`
* remarks: The definition covers the case `A = -int_Γ p*dV` where `Γ` is a curve in the phase space and implies that work generally depends upon `Γ`, and that type of process must be defined (e.g. isentropic or isothermic).
*/
}
alias work for mechanicalWork;
/* ISO-80000-4 item 4-29 mechanical efficiency */
attribute def MechanicalEfficiencyValue :> DimensionOneValue {
doc
/*
* source: item 4-29 mechanical efficiency
* symbol(s): `η`
* application domain: mechanics
* name: MechanicalEfficiency (specializes DimensionOneQuantity)
* quantity dimension: 1
* measurement unit(s): 1
* tensor order: 0
* definition: quotient of output power `P_"out"` (item 4-27) from a system and input power `P_"in"` (item 4-27) to this system: `η = P_"out"/P_"in"`
* remarks: The system must be specified. This quantity is often expressed by the unit percent, symbol %.
*/
}
attribute mechanicalEfficiency: MechanicalEfficiencyValue :> scalarQuantities;
/* ISO-80000-4 item 4-30.1 mass flow */
attribute def MassFlowValue :> ScalarQuantityValue {
doc
/*
* source: item 4-30.1 mass flow (magnitude)
* symbol(s): `j_m`
* application domain: generic
* name: MassFlow
* quantity dimension: L^-2*M^1*T^-1
* measurement unit(s): kg*m^-2*s^-1
* tensor order: 0
* definition: vector (ISO 80000-2) quantity characterizing a flowing fluid by the product of its local mass density `ρ` (item 4-2) and local velocity `vec(v)` (ISO 80000-3): `vec(j_m) = ρ vec(v)`
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: MassFlowUnit[1];
}
attribute massFlow: MassFlowValue[*] nonunique :> scalarQuantities;
attribute def MassFlowUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = -2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
attribute def Cartesian3dMassFlowVector :> VectorQuantityValue {
doc
/*
* source: item 4-30.1 mass flow (vector)
* symbol(s): `vec(j_m)`
* application domain: generic
* name: MassFlow
* quantity dimension: L^-2*M^1*T^-1
* measurement unit(s): kg*m^-2*s^-1
* tensor order: 1
* definition: vector (ISO 80000-2) quantity characterizing a flowing fluid by the product of its local mass density `ρ` (item 4-2) and local velocity `vec(v)` (ISO 80000-3): `vec(j_m) = ρ vec(v)`
* remarks: None.
*/
attribute :>> isBound = false;
attribute :>> num: Real[3];
attribute :>> mRef: Cartesian3dMassFlowCoordinateFrame[1];
}
attribute massFlowVector: Cartesian3dMassFlowVector :> vectorQuantities;
attribute def Cartesian3dMassFlowCoordinateFrame :> VectorMeasurementReference {
attribute :>> dimensions = 3;
attribute :>> isBound = false;
attribute :>> isOrthogonal = true;
attribute :>> mRefs: MassFlowUnit[3];
}
/* ISO-80000-4 item 4-30.2 mass flow rate */
attribute def MassFlowRateValue :> ScalarQuantityValue {
doc
/*
* source: item 4-30.2 mass flow rate
* symbol(s): `q_m`
* application domain: generic
* name: MassFlowRate
* quantity dimension: M^1*T^-1
* measurement unit(s): kg*s^-1
* tensor order: 0
* definition: scalar (ISO 80000-2) quantity characterizing the total flow through the two-dimensional domain `A` with normal vector `vec(e)_n` of a flowing fluid with mass flow `vec(j)_m` (item 4-30.1) as an integral: `q_m = int int_A vec(j)_m * vec(e)_n dA` where `dA` is the area (ISO 80000-3) of an element of the two-dimensional domain `A`
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: MassFlowRateUnit[1];
}
attribute massFlowRate: MassFlowRateValue[*] nonunique :> scalarQuantities;
attribute def MassFlowRateUnit :> DerivedUnit {
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (massPF, durationPF); }
}
/* ISO-80000-4 item 4-30.3 mass change rate */
attribute def MassChangeRateValue :> ScalarQuantityValue {
doc
/*
* source: item 4-30.3 mass change rate
* symbol(s): `q_m`
* application domain: generic
* name: MassChangeRate
* quantity dimension: M^1*T^-1
* measurement unit(s): kg*s^-1
* tensor order: 0
* definition: rate of increment of mass `m` (item 4-1): `q_m = (dm)/(dt)` where `dm` is the infinitesimal mass (item 4-1) increment and `dt` is the infinitesimal duration (ISO 80000-3)
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: MassChangeRateUnit[1];
}
attribute massChangeRate: MassChangeRateValue[*] nonunique :> scalarQuantities;
attribute def MassChangeRateUnit :> DerivedUnit {
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (massPF, durationPF); }
}
/* ISO-80000-4 item 4-31 volume flow rate */
attribute def VolumeFlowRateValue :> ScalarQuantityValue {
doc
/*
* source: item 4-31 volume flow rate
* symbol(s): `q_v`
* application domain: generic
* name: VolumeFlowRate
* quantity dimension: L^3*T^-1
* measurement unit(s): m^3*s^-1
* tensor order: 0
* definition: scalar (ISO 80000-2) quantity characterizing the total flow through the two-dimensional domain `A` with the normal vector `vec(e)_n` of a flowing fluid with velocity `vec(v)` (ISO 80000-3) as an integral: `q_v = int int_A vec(v) * vec(e)_n dA` where `dA` is the area (ISO 80000-3) of an element of the two-dimensional domain `A`
* remarks: None.
*/
attribute :>> num: Real;
attribute :>> mRef: VolumeFlowRateUnit[1];
}
attribute volumeFlowRate: VolumeFlowRateValue[*] nonunique :> scalarQuantities;
attribute def VolumeFlowRateUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 3; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, durationPF); }
}
/* ISO-80000-4 item 4-32 action quantity */
attribute def ActionQuantityValue :> ScalarQuantityValue {
doc
/*
* source: item 4-32 action quantity
* symbol(s): `S`
* application domain: generic
* name: ActionQuantity
* quantity dimension: L^2*M^1*T^-1
* measurement unit(s): J*s, kg*m^2*s^-1
* tensor order: 0
* definition: time integral of energy `E` over a time interval `(t_1, t_2)`: `S = int_(t_1)^(t_2) E dt`
* remarks: The energy may be expressed by a Lagrangian or Hamiltonian function.
*/
attribute :>> num: Real;
attribute :>> mRef: ActionQuantityUnit[1];
}
attribute actionQuantity: ActionQuantityValue[*] nonunique :> scalarQuantities;
attribute def ActionQuantityUnit :> DerivedUnit {
private attribute lengthPF: QuantityPowerFactor[1] { :>> quantity = isq.L; :>> exponent = 2; }
private attribute massPF: QuantityPowerFactor[1] { :>> quantity = isq.M; :>> exponent = 1; }
private attribute durationPF: QuantityPowerFactor[1] { :>> quantity = isq.T; :>> exponent = -1; }
attribute :>> quantityDimension { :>> quantityPowerFactors = (lengthPF, massPF, durationPF); }
}
}
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