# Inertia

Mass and inertia tensor of solid mass

• Library:
• Body Elements

## Description

The Inertia block adds the inertial properties of a point or distributed mass to the attached frame. The inertia type depends on the parameterization selected. A ```Point Mass``` parameterization enables you to model a concentrated mass with no rotational inertia. A `Custom` parameterization enables you to model a distributed mass with the specified moments and products of inertia. An inertia icon identifies the inertia location in the Mechanics Explorer visualization pane.

## Ports

### Frame

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Local reference frame of the inertia element. Connect to a frame line or frame port to define the relative position and orientation of the inertia.

## Parameters

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Inertia parameterization to use. Select `Point Mass` to represent a mass with no rotational inertia. Select `Custom` to represent a distributed mass with rotational inertia.

Aggregate mass of the solid. The mass can be a positive or negative value. Specify a negative mass to model the aggregate effect of voids and cavities in a compound body.

[x y z] coordinates of the center of mass relative to the block reference frame. The center of mass coincides with the center of gravity in uniform gravitational fields only.

Three-element vector with the [Ixx Iyy Izz] moments of inertia specified relative to a frame with origin at the center of mass and axes parallel to the block reference frame. The moments of inertia are the diagonal elements of the inertia tensor

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

where:

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

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

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

Three-element vector with the [Iyz Izx Ixy] products of inertia specified relative to a frame with origin at the center of mass and axes parallel to the block reference frame. The products of inertia are the off-diagonal elements of the inertia tensor

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

where:

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

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

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