# 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:

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

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

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

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:

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

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

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

### Graphic

Type of graphic to use in the visualization of the inertia, specified as `Marker` or `None`. Set this parameter to `Marker` to represent the inertia as a marker, and set this parameter to `None` to hide the inertia from the model visualization.

Shape of the marker, specified as ```Inertia Icon```, `Sphere`, `Cube`, or `Frame`. The motion of the marker reflects the motion of the inertia itself.

#### Dependencies

To enable this parameter, set Type to `Marker`.

Width of the marker in pixels, specified as a scalar. 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.

#### Dependencies

To enable this parameter, set Type to `Marker`.

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 `Marker`.

Color of the light due to diffuse reflection, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. 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 Type to `Marker`.

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`

Color of the light due to specular reflection, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. 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 `Marker`

2. Visual Properties to `Advanced`

Color of the ambient light, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

Ambient light refers to a general level of illumination that does not come directly from a light source. The Ambient light consists of light that has been reflected and re-reflected so many times that it is no longer coming from any particular direction.

#### Dependencies

To enable this parameter, set:

1. Type to `Marker`

2. Visual Properties to `Advanced`

Color due to self illumination, specified as an [R,G,B] or [R,G,B,A] vector in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

The emission color is color that does not come from any external source, and therefore seems to be emitted by the marker itself. When a marker has a emissive color, the marker can be seen even if there is no external light source.

#### Dependencies

To enable this parameter, set:

1. Type to `Marker`

2. Visual Properties to `Advanced`

Shininess of the marker, specified as a scalar in the range of 0 to 128. This parameter affects the sharpness of the specular reflections of the marker. A marker with high shininess has a mirror-like appearance, and marker with low shininess has a more low-gloss or satin appearance.

#### Dependencies

To enable this parameter, set:

1. Type to `Marker`

2. Visual Properties to `Advanced`

## Version History

Introduced in R2012a