# Inertia

Mass element with fixed inertial properties

• Library:
• Simscape / Multibody / Body Elements

## Description

The Inertia block adds to the attached frame a point or distributed mass with fixed inertial properties. The type of mass (point or distributed) depends on the parameterization selected for the block. A selection of ```Point Mass``` assumes the mass to be concentrated at a point and therefore devoid of rotational inertia. A selection of `Custom` assumes the mass to be distributed in space, allowing it to possess nonzero moments of inertia, products of inertia, and center-of-mass coordinates (the latter against the reference frame of the block).

A choice of marker provides a means to identify the inertia in the model visualization. The visualization opens (by default) in Mechanics Explorer at the start of simulation or upon diagram update. Use the marker to track the motion of the inertia against the remainder of the model. Various marker shapes are available—an inertia icon, a sphere, a cube, a frame—each with configurable dimensions. To eliminate the inertia from the model visualization (while retaining its effects on the model dynamics), the block provides an option of `None`.

## 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

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.

Total mass to attribute to the solid element. This parameter can be positive or negative. Use a negative value to capture the effect of a void or cavity in a compound body (one comprising multiple solids and inertias), being careful to ensure that the mass of the body is on the whole positive.

[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:

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

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

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

Graphic

Choice of graphic to use in the visualization of the inertia. The graphic is by default a simple marker, specifically an inertia icon. Other markers are available, these encompassing spheres, cubes, and frames. Change this parameter to `None` to eliminate the inertia altogether from the model visualization.

Shape of the marker by means of which to visualize the inertia. The motion of the marker reflects the motion of the inertia itself.

Width of the marker in pixels. This width does not scale with zoom level. Note that the apparent size of the marker depends partly on screen resolution, with higher resolutions packing more pixels per unit length, and therefore producing smaller icons.

Parameterizations for specifying visual properties. Select `Simple` to specify diffuse color and opacity. Select `Advanced` to specify more visual properties, such as Specular Color, Ambient Color, Emissive Color, and Shininess.

#### Dependencies

To enable this parameter, set Type to ```From Geometry``` or `Marker`.

RGB color vector with red (R), green (G), and blue (B) color amounts specified on a 0–1 scale. A color picker provides an alternative interactive means of specifying a color. If you change the Visual Properties setting to `Advanced`, the color specified in this parameter becomes the Diffuse Color vector.

#### Dependencies

To enable this parameter, set :

1. Type to `Marker`.

2. Visual Properties to `Simple`.

Graphic opacity, specified as a scalar in the range of 0 to 1. A scalar of 0 corresponds to completely transparent, and a scalar of 1 corresponds to completely opaque.

#### Dependencies

To enable this parameter, set:

1. Type to `Marker`

2. Visual Properties to `Simple`

True color under direct white light specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. An optional fourth element specifies the color opacity also on a scale of 0–1. Omitting the opacity element is equivalent to specifying a value of `1`.

#### Dependencies

To enable this parameter, set :

1. Type to `Marker`.

2. Visual Properties to `Advanced`.

Color of specular highlights, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

#### Dependencies

To enable this parameter, set:

1. Type to `From Geometry` or `Marker`

2. Visual Properties to `Advanced`

Color of shadow areas in diffuse ambient light, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

#### Dependencies

To enable this parameter, set:

1. Type to `From Geometry` or `Marker`

2. Visual Properties to `Advanced`

Graphic color due to self illumination, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element (A) specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

#### Dependencies

To enable this parameter, set:

1. Type to `From Geometry` or `Marker`

2. Visual Properties to `Advanced`

Sharpness of specular light reflections, specified as a scalar number on a 0–128 scale. Increase the shininess value for smaller but sharper highlights. Decrease the value for larger but smoother highlights.

#### Dependencies

To enable this parameter, set:

1. Type to `From Geometry` or `Marker`

2. Visual Properties to `Advanced`