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

expand all

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

expand all

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

expand all

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:

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

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:

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

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 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 — Shape of marker to represent to variable mass
`Sphere` (default) | `Cube` | `Frame`

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.

Size — Width of the marker in pixels
10 `pixels` (default) | scalar

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.

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

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.

Diffuse Color — Color of light due to diffuse reflection
[0.5 0.5 0.5] (default) | 3-by-1 or 1-by-3 vector with values in the range of 0 to 1 | 4-by-1 or 1-by-4 vector with values in the range of 0 to 1

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

Opacity — Graphic opacity
1.0 (default) | scalar in the range of 0 to 1

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.