# General Variable Mass

Mass element with variable inertial properties

Libraries:
Simscape / Multibody / Body Elements / Variable Mass

## Description

The General Variable Mass block adds to the attached frame a mass element with constant or time-varying inertial properties. The mass element can be a point mass without rotational inertia or a custom mass with rotational inertia. The inertial properties include mass, center of mass, moments of inertia, and products of inertia. Each inertial property can be independently configured as constant or time-varying.

The geometry of the mass element is unspecified. A marker or equivalent inertia ellipsoid identifies the mass element in the visualization pane of Mechanics Explorer. An inertia ellipsoid provides a graphical representation of the principal moments of inertia of the mass element. The block includes an option to hide the variable mass element in the Mechanics Explorer visualization window.

## Limitations

• The General Variable Mass block does not conserve the angular momentum when simulated without an external moment. Instead of the angular momentum, the angular velocity remains unchanged.

## Ports

### Input

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Input port for the time-varying mass.

#### Dependencies

This port is enabled when the Inertia > Mass parameter is set to `Time-Varying`.

Input port for the time-varying center-of-mass coordinates. Specify the coordinates in the order `[x y z]` relative to the block reference frame.

#### Dependencies

This port is enabled when the Inertia > Center of Mass parameter is set to `Time-Varying`.

Input port for the time-varying inertia tensor. Specify the tensor elements in the order ```[Ixx Ixy I xz; Iyx Iyy Iyz; Izx Izy Izz]```. The elements are defined relative to a frame with origin at the center of mass and axes aligned with the reference frame. See the Inertia tensor parameter description for the definitions of the moments and products of inertia.

#### Dependencies

This port is enabled when the Inertia > Type parameter is set to `Custom`.

### Frame

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

## Parameters

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### Inertia

Choice of point or distributed mass. Select ```Point Mass``` to model a concentrated mass with no rotational inertia. Select `Custom` to model a distributed mass with the specified inertia tensor and center of mass.

Choice of fixed or variable mass. Select `Time-Varying` to specify the mass as a variable using physical signal input port m. Select `Constant` to specify the mass as a constant parameter.

Aggregate mass of the mass element. 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. The mass is constant when this parameter is active.

#### Dependencies

This parameter is enabled when the Mass parameter is set to `Constant`.

Choice of fixed or variable center of mass. Select `Time-Varying` to specify the center of mass as a variable using physical signal input port com. Select `Constant` to specify the center of mass as a constant parameter.

[x y z] coordinates of the center of mass relative to the origin of the reference frame. The center of mass coincides with the center of gravity in uniform gravitational fields only. The center of mass is constant when this parameter is active.

#### Dependencies

This parameter is enabled when the Center of Mass parameter is set to `Constant`.

Choice of a variable or fixed inertia matrix. Select `Time-Varying` to specify the inertia matrix as a variable using physical signal input port I. Select `Constant` to specify the moments and products of inertia separately as constant block parameters.

Moments of inertia of the variable mass element specified in the order [Ixx Iyy Izz]. The moments of inertia are defined relative to a frame with origin at the center of mass and with axes parallel to the reference frame axes. 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:

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

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

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

#### Dependencies

This parameter is enabled when the Inertia Matrix parameter is set to `Constant`.

Products of inertia of the variable mass element specified in the order [Iyz Izx Ixy]. The products of inertia are defined relative to a frame with origin at the center of mass and with axes parallel to the reference frame axes. The products of inertia are the off-diagonal elements of the inertia matrix,

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

where:

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

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

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

#### Dependencies

This parameter is enabled when the Inertia Matrix parameter is set to `Constant`.

### Graphic

Visualization setting for this variable mass, specified as `Equivalent Inertia Ellipsoid`, `Marker`, or `None`. Set the parameter to `Equivalent Inertia Ellipsoid` to represent the variable mass as an ellipsoid. Set the parameter to `Marker` to represent the variable mass as a marker. Set the parameter to `None` to hide the variable mass in the model visualization.

Shape of the marker by means of which to visualize the variable mass, specified as `Sphere`, `Cube`, or `Frame`. The motion of the marker reflects the motion of the variable mass itself.

#### Dependencies

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

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.

#### 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 `Equivalent Inertia Ellipsoid` or `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.

The diffuse color reflects the main color of the graphic and provides shading that gives the graphic a three-dimensional appearance.

#### Dependencies

To enable this parameter, set Type to `From Geometry` or `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 ```Equivalent Inertia Ellipsoid``` or `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. This parameter changes the color of the specular highlight, which is the bright spot on the graphic due to the reflection of the light from the light source.

#### Dependencies

To enable this parameter, set:

1. Type to ```Equivalent Inertia Ellipsoid``` or `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. You can adjust this parameter to change the shadow color of the graphic.

#### Dependencies

To enable this parameter, set:

1. Type to ```Equivalent Inertia Ellipsoid``` or `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 graphic itself. When a graphic has a emissive color, the graphic can be seen even if there is no external light source.

#### Dependencies

To enable this parameter, set:

1. Type to ```Equivalent Inertia Ellipsoid``` 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 ```Equivalent Inertia Ellipsoid``` or `Marker`

2. Visual Properties to `Advanced`

## Version History

Introduced in R2016b