simscape.multibody.MassDistribution Class

R2026b

Namespace: simscape.multibody

Mass distribution computation object

Since R2022a

Description

A simscape.multibody.MassDistribution object stores mass distribution properties relative to an implicit reference frame. Obtain a MassDistribution object by calling the massDistribution method on a simscape.multibody.GeneralSolid, simscape.multibody.UniformSolid, or simscape.multibody.GeneralInertia object, or construct one directly. When obtained from a solid, the implicit reference frame coincides with the reference frame of the solid.

Class Attributes

Sealed	true
ConstructOnLoad	true
RestrictsSubclassing	true

For information on class attributes, see Class Attributes.

Creation

Description

MD = simscape.multibody.MassDistribution creates a mass distribution object with default property values.

MD = simscape.multibody.MassDistribution(mass) creates a mass distribution object with the specified mass.

MD = simscape.multibody.MassDistribution(mass,com) creates a mass distribution object with the specified mass and center of mass.

MD = simscape.multibody.MassDistribution(mass,com,moi) creates a mass distribution object with the specified mass, center of mass, and moments of inertia.

MD = simscape.multibody.MassDistribution(mass,com,moi,poi) creates a mass distribution object with the specified mass, center of mass, moments of inertia, and products of inertia.

Properties

Mass — Total mass

simscape.Value(1,"kg") (default) | simscape.Value(M,"Mass unit")

Total mass, specified as a simscape.Value object that represents a positive scalar with a unit of mass.

Example: simscape.Value(16,"lbm")

Attributes:

GetAccess	public
SetAccess	public
NonCopyable	true

CenterOfMass — Center of mass position

simscape.Value([0 0 0]',"m") (default) | simscape.Value([x y z],"Length unit") | simscape.Value([x y z]',"Length unit")

Center of mass position relative to the reference frame origin, along the axes of the reference frame, specified as a simscape.Value object that represents a 3-by-1 or 1-by-3 array with a unit of length.

Example: simscape.Value([0 0 5],"mm")

Attributes:

GetAccess	public
SetAccess	public
NonCopyable	true

MomentsOfInertia — Diagonal elements of inertia matrix

simscape.Value([0 0 0]',"kg*m^2") (default) | simscape.Value([I_xx I_yy I_zz],"mass*length^2") | simscape.Value([I_xx I_yy I_zz]',"mass*length^2")

Moments of inertia about the center of mass, expressed in the reference frame axes, specified as a simscape.Value object that represents a 3-by-1 or 1-by-3 array with a unit of mass*length^2. The three elements correspond to [I_xx I_yy I_zz].

The moments of inertia are the diagonal elements of the inertia matrix

$$\left(\begin{array}{ccc}{I}_{xx}& & \\ & I_{yy}& \\ & & I_{zz}\end{array}\right),$$

where:

• $$I_{xx}={\displaystyle \underset{m}{\int }\left(y^2+z^2\right)dm}$$

• $$I_{yy}={\displaystyle \underset{m}{\int }\left(x^2+z^2\right)dm}$$

• $$I_{zz}={\displaystyle \underset{m}{\int }\left(x^2+y^2\right)dm}$$

Example: simscape.Value([12 15 10],"kg*cm^2")

Attributes:

GetAccess	public
SetAccess	public
NonCopyable	true

ProductsOfInertia — Off-diagonal elements of inertia matrix

simscape.Value([0 0 0]',"kg*m^2") (default) | simscape.Value([I_yz I_zx I_xy],"mass*length^2") | simscape.Value([I_yz I_zx I_xy]',"mass*length^2")

Products of inertia about the center of mass, expressed in the reference frame axes, specified as a simscape.Value object that represents a 3-by-1 or 1-by-3 array with a unit of mass*length^2. The three elements correspond to [I_yz I_zx I_xy].

The products of inertia are the off-diagonal elements of the inertia matrix

$$\left(\begin{array}{ccc}& I_{xy}& I_{zx}\\ I_{xy}& & I_{yz}\\ I_{zx}& I_{yz}& \end{array}\right),$$

where:

• $$I_{yz}=-{\displaystyle \underset{m}{\int }yzdm}$$

• $$I_{zx}=-{\displaystyle \underset{m}{\int }zxdm}$$

• $$I_{xy}=-{\displaystyle \underset{m}{\int }xydm}$$

Example: simscape.Value([-2 3 1],"kg*cm^2")

Attributes:

GetAccess	public
SetAccess	public
NonCopyable	true

Methods

Public Methods

inertiaMatrix	Compute inertia matrix
principalMomentsOfInertia	Compute principal moments of inertia
principalToReferenceTransformation	Compute 3-D rigid transformation between principal and reference frames
transform	Transform inertia to different frame

Examples

Query Inertia Properties of a Mass Distribution

Create a mass distribution object and compute its inertia matrix and principal moments of inertia.

Create a MassDistribution object with a mass of 3 kg, a center of mass at [0.05 0 0.02] m, moments of inertia of [0.1 0.15 0.2] kg*m^2, and products of inertia of [0.01 -0.02 0.005] kg*m^2.

md = simscape.multibody.MassDistribution( ...
    simscape.Value(3,"kg"), ...
    simscape.Value([0.05 0 0.02],"m"), ...
    simscape.Value([0.1 0.15 0.2],"kg*m^2"), ...
    simscape.Value([0.01 -0.02 0.005],"kg*m^2"))

md =
  MassDistribution with properties:

                 Mass: 3 (kg)
         CenterOfMass: [0.0500 0 0.0200] (m)
     MomentsOfInertia: [0.1000 0.1500 0.2000] (kg*m^2)
    ProductsOfInertia: [0.0100 -0.0200 0.0050] (kg*m^2)

Compute the full 3-by-3 inertia matrix of the mass distribution.

IM = inertiaMatrix(md)

IM =
    0.1000    0.0050   -0.0200
    0.0050    0.1500    0.0100
   -0.0200    0.0100    0.2000

    (kg*m^2)

Compute the principal moments of inertia. These are the eigenvalues of the inertia matrix, representing the moments of inertia about the principal axes.

PM = principalMomentsOfInertia(md)

PM =
    0.0953    0.1494    0.2053

    (kg*m^2)

Compute the transformation from the principal frame to the reference frame. The translation component equals the center of mass position, and the rotation aligns the principal axes with the reference frame axes.

T = principalToReferenceTransformation(md)

T =
  Transformation:

       Rotation: [0.9903 -0.0739 -0.0946 -0.0702]
    Translation: [0.0500 0 0.0200] (m)

Version History

Introduced in R2022a