Inertial properties of a solid or mass disturbance

Body Elements

This block represents the inertial properties of a solid. The
solid can be a point mass or a 3-D mass distribution. To represent
the inertial properties of a point mass, the dialog box provides a ```
Point
Mass
```

parameterization. Inertial parameters of a point
mass include only the total mass of the solid. To represent the inertial
properties of a 3-D mass distribution, the dialog box provides a `Custom`

parameterization.
Inertial parameters of a custom inertia include the total mass of
the solid, its center of mass, as well as its moments and products
of inertia.

This block can also represent a mass disturbance in a model. The disturbance can have positive or negative inertia. A disturbance with negative inertia reduces the total inertia of the rigid body the block connects to. A disturbance with positive inertia increases the total inertia of the rigid body the block connects to. Use this block to adjust the total inertia of a rigid body.

The visualization pane of Mechanics Explorer identifies the position of an Inertia element with the inertia icon .

The dialog box contains a **Properties** area
with inertia options and parameters.

**Type**Select a method to specify inertia. The default is

`Point Mass`

.Type Description `Point Mass`

Treat the inertia as a mass with zero volume. The point mass is located at the reference frame origin. `Custom`

Manually specify all inertial parameters, including mass, center of mass, and moments and products of inertia.

`Point Mass`

/`Custom`

:**Mass**Enter the total mass of the solid. Select a physical unit. The default is

`1 Kg`

.`Custom`

:**Center of Mass**Enter the center of mass coordinates with respect to the solid reference frame in the order [X Y Z]. In a uniform gravitational field, the center of mass coincides with the center of gravity. Select a physical unit. The default is

`[0 0 0]`

.`Custom`

:**Moments of Inertia**Enter the mass moments of inertia of the solid element in the order [I

_{xx}, I_{yy}, I_{zz}]. Each moment of inertia must refer to a frame whose axes are parallel to the block reference frame axes and whose origin is coincident with the solid center of mass. The moments of inertia are the diagonal elements of the solid inertia tensor,$$\left(\begin{array}{ccc}{I}_{xx}& & \\ & {I}_{yy}& \\ & & {I}_{zz}\end{array}\right),$$

where:

$${I}_{xx}={\displaystyle \underset{V}{\int}\left({y}^{2}+{z}^{2}\right)\text{\hspace{0.17em}}dm}$$

$${I}_{yy}={\displaystyle \underset{V}{\int}\left({x}^{2}+{z}^{2}\right)\text{\hspace{0.17em}}dm}$$

$${I}_{zz}={\displaystyle \underset{V}{\int}\left({x}^{2}+{y}^{2}\right)\text{\hspace{0.17em}}dm}$$

Select a physical unit. The default is

`[1 1 1] kg*m^2`

.`Custom`

:**Products of Inertia**Enter the mass products of inertia of the solid element in the order [I

_{yz}, I_{zx}, I_{xy}]. Each product of inertia must refer to a frame whose axes are parallel to the block reference frame axes and whose origin is coincident with the solid center of mass. The products of inertia are the off-diagonal elements of the solid inertia tensor,$$\left(\begin{array}{ccc}& {I}_{xy}& {I}_{zx}\\ {I}_{xy}& & {I}_{yz}\\ {I}_{zx}& {I}_{yz}& \end{array}\right),$$

where:

$${I}_{yz}=-{\displaystyle \underset{V}{\int}yz\text{\hspace{0.17em}}dm}$$

$${I}_{zx}=-{\displaystyle \underset{V}{\int}zx\text{\hspace{0.17em}}dm}$$

$${I}_{xy}=-{\displaystyle \underset{V}{\int}xy\text{\hspace{0.17em}}dm}$$

Select a physical unit. The default is

`[0 0 0] kg*m^2`

.

This block contains frame port R, representing the inertia reference frame.

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