# General Variable Mass

Mass element with variable inertial properties

• Library:
• 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:

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

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

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

#### 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:

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

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

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

#### Dependencies

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

#### Graphic

Visualization setting for this solid. Marker dimensions are fixed and specified in pixel units. Ellipsoid dimensions are variable and depend on the specified mass and inertia tensor. The center of the ellipsoid coincides with the specified center of mass. Marker visualization is active on model update and during simulation. Ellipsoid visualization is active during simulation only.

Geometrical shape of the graphic marker. Mechanics Explorer shows the marker using the selected shape.

Size of the marker in units of pixels. The size does not change with zoom level.

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`.

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 on a scale of 0–1. An opacity of `0` corresponds to a completely transparent graphic and an opacity of `1` to a completely opaque graphic.

#### 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 `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 `Marker`.

2. Visual Properties to `Advanced`.

Surface 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 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`.

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 `Marker`.

2. Visual Properties to `Advanced`.