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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`R` — Reference frame
frame

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

`Type` — Inertia parameterization to use
`Point Mass` (default) | `Custom`

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.

`Mass` — Total mass of the solid element
`1 kg` (default) | scalar with units of mass

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.

`Custom: Center of Mass` — Center-of-mass coordinates
`[0 0 0] m` (default) | three-element vector with units of length

[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.

`Custom: Moments of Inertia` — Diagonal elements of inertia tensor
`[1 1 1] kgm^2` (default) | three-element vector with units of masslength^2

Three-element vector with the [I_xx I_yy I_zz] 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

$(\begin{matrix} I_{x x} \\ I_{y y} \\ I_{z z} \end{matrix}),$

where:

$I_{x x} = \int_{V} (y^{2} + z^{2}) d m$
$I_{y y} = \int_{V} (x^{2} + z^{2}) d m$
$I_{z z} = \int_{V} (x^{2} + y^{2}) d m$

`Custom: Products of Inertia` — Off-diagonal elements of inertia tensor
`[0 0 0] kgm^2` (default) | three-element vector with units of masslength^2

Three-element vector with the [I_yz I_zx I_xy] 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

$(\begin{matrix} I_{x y} & I_{z x} \\ I_{x y} & I_{y z} \\ I_{z x} & I_{y z} \end{matrix}),$

where:

$I_{y z} = - \int_{V} y z d m$
$I_{z x} = - \int_{V} z x d m$
$I_{x y} = - \int_{V} x y d m$

Graphic

`Type` — Graphic to use in the visualization of the inertia
`Marker` (default) | `None`

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.

`Marker: Shape` — Shape of the marker to assign to the inertia
`Inertia Icon` (default) | `Sphere` | `Cube` | `Frame`

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

`Marker: Size` — Width of the marker in pixels
`10` (default) | scalar with units of pixels

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.

`Visual Properties` — Parameterizations for color and opacity
`Simple` (default) | `Advanced`

Parameterization for specifying visual properties. Select Simple to specify color and opacity. Select Advanced to add specular highlights, ambient shadows, and self-illumination effects.

Dependencies

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

`Color` — True color as [R,G,B] vector on 0–1 scale
`[0.5 0.5 0.5]` (default) | three-element vector with values constrained to 0–1

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.