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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`m` — Mass
physical signal specified as a scalar with units of mass

Input port for the time-varying mass.

Dependencies

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

`com` — Center of mass
physical signal specified as a 3-by-1 or 1-by-3 vector with units of length

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.

`I` — Inertia
physical signal specified as a 3-by-3 matrix with units of mass × length^2

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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`R` — Reference frame
frame

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

`Type` — Choice of point or distributed mass
`Custom` (default) | `Point Mass`

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.

`Mass` — Mass parameterization
`Time-Varying` (default) | `Constant`

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.

`Mass: Value` — Aggregate mass of the mass element
`1 kg` (default) | scalar with units of mass

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.

`Center of Mass` — Center-of-mass parameterization
`Time-Varying` (default) | `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.

`Center of Mass: Value` — 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 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.

`Inertia Matrix` — Inertia-matrix parameterization
`Time-Varying` (default) | `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.

`Inertia Matrix: Moments of Inertia` — Diagonal elements of the inertia matrix
`[1 1 1] kg * m^2` (default) | three-element vector with units of mass*length^2

Moments of inertia of the variable mass element specified in the order [I_xx I_yy I_zz]. 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,

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

where:

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

Dependencies

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

`Inertia Matrix: Products of Inertia` — Off-diagonal elements of the inertia matrix
`[0 0 0] kg * m^2` (default) | 3-element array with units of mass * length^2

Products of inertia of the variable mass element specified in the order [I_yz I_zx I_xy]. 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,

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

where:

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

Dependencies

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

Graphic

`Type` — Geometry type to use in model visualizations
`Equivalent Inertia Ellipsoid` (default) | `Marker` | `None`

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.

`Marker: Shape` — Shape of the graphic marker
`Sphere` (default) | `Cube` | `Frame`

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

`Marker: Size` — Pixel size of the graphic marker
`10` (default) | scalar with units of pixels

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

`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.