BodyRigid body with mass, inertia tensor and one frame connector (12 potential states) 
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Rigid body with mass and inertia tensor. All parameter vectors have to be resolved in frame_a. The inertia tensor has to be defined with respect to a coordinate system that is parallel to frame_a with the origin at the center of mass of the body.
By default, this component is visualized by a cylinder located between frame_a and the center of mass and by a sphere that has its center at the center of mass. If the cylinder length is smaller as the radius of the sphere, e.g., since frame_a is located at the center of mass, the cylinder is not displayed. Note, that the animation may be switched off via parameter animation = false.
States of Body Components
Every body has potential states. If possible a tool will select the states of joints and not the states of bodies because this is usually the most efficient choice. In this case the position, orientation, velocity and angular velocity of frame_a of the body will be computed by the component that is connected to frame_a. However, if a body is moving freely in space, variables of the body have to be used as states. The potential states of the body are:
The quaternions have the slight disadvantage that there is a nonlinear constraint equation between the 4 quaternions. Therefore, at least one nonlinear equation has to be solved during simulation. A tool might, however, analytically solve this simple constraint equation. Using the 3 angles as states has the disadvantage that there is a singular configuration in which a division by zero will occur. If it is possible to determine in advance for an application class that this singular configuration is outside of the operating region, the 3 angles might be used as potential states by setting useQuaternions = false.
In text books about 3dimensional mechanics often 3 angles and the angular velocity are used as states. This is not the case here, since 3 angles and their derivatives are used as potential states (if useQuaternions = false). The reason is that for realtime simulation the discretization formula of the integrator might be "inlined" and solved together with the body equations. By appropriate symbolic transformation the performance is drastically increased if angles and their derivatives are used as states, instead of angles and the angular velocity.
Whether or not variables of the body are used as states is usually automatically selected by the Modelica translator. If parameter enforceStates is set to true in the "Advanced" menu, then body variables are forced to be used as states according to the setting of parameters "useQuaternions" and "sequence_angleStates".
animation 
Value: true Type: Boolean Description: = true, if animation shall be enabled (show cylinder and sphere) 

r_CM 
Value: Type: Position[3] (m) Description: Vector from frame_a to center of mass, resolved in frame_a 
m 
Value: Type: Mass (kg) Description: Mass of rigid body 
I_11 
Value: 0.001 Type: Inertia (kg·m²) Description: (1,1) element of inertia tensor 
I_22 
Value: 0.001 Type: Inertia (kg·m²) Description: (2,2) element of inertia tensor 
I_33 
Value: 0.001 Type: Inertia (kg·m²) Description: (3,3) element of inertia tensor 
I_21 
Value: 0 Type: Inertia (kg·m²) Description: (2,1) element of inertia tensor 
I_31 
Value: 0 Type: Inertia (kg·m²) Description: (3,1) element of inertia tensor 
I_32 
Value: 0 Type: Inertia (kg·m²) Description: (3,2) element of inertia tensor 
angles_fixed 
Value: false Type: Boolean Description: = true, if angles_start are used as initial values, else as guess values 
angles_start 
Value: {0, 0, 0} Type: Angle[3] (rad) Description: Initial values of angles to rotate frame_a around 'sequence_start' axes into frame_b 
sequence_start 
Value: {1, 2, 3} Type: RotationSequence Description: Sequence of rotations to rotate frame_a into frame_b at initial time 
w_0_fixed 
Value: false Type: Boolean Description: = true, if w_0_start are used as initial values, else as guess values 
w_0_start 
Value: {0, 0, 0} Type: AngularVelocity[3] (rad/s) Description: Initial or guess values of angular velocity of frame_a resolved in world frame 
z_0_fixed 
Value: false Type: Boolean Description: = true, if z_0_start are used as initial values, else as guess values 
z_0_start 
Value: {0, 0, 0} Type: AngularAcceleration[3] (rad/s²) Description: Initial values of angular acceleration z_0 = der(w_0) 
sphereDiameter 
Value: world.defaultBodyDiameter Type: Diameter (m) Description: Diameter of sphere 
cylinderDiameter 
Value: sphereDiameter / Types.Defaults.BodyCylinderDiameterFraction Type: Diameter (m) Description: Diameter of cylinder 
sequence_angleStates 
Value: {1, 2, 3} Type: RotationSequence Description: Sequence of rotations to rotate world frame into frame_a around the 3 angles used as potential states 
I 
Value: [I_11, I_21, I_31; I_21, I_22, I_32; I_31, I_32, I_33] Type: Inertia[3,3] (kg·m²) Description: inertia tensor 
R_start 
Value: Modelica.Mechanics.MultiBody.Frames.axesRotations(sequence_start, angles_start, zeros(3)) Type: Orientation Description: Orientation object from world frame to frame_a at initial time 
z_a_start 
Value: Frames.resolve2(R_start, z_0_start) Type: AngularAcceleration[3] (rad/s²) Description: Initial values of angular acceleration z_a = der(w_a), i.e., time derivative of angular velocity resolved in frame_a 
sphereColor 
Default Value: Modelica.Mechanics.MultiBody.Types.Defaults.BodyColor Type: Color Description: Color of sphere 

cylinderColor 
Default Value: sphereColor Type: Color Description: Color of cylinder 
specularCoefficient 
Default Value: world.defaultSpecularCoefficient Type: SpecularCoefficient Description: Reflection of ambient light (= 0: light is completely absorbed) 
frame_a 
Type: Frame_a Description: Coordinate system fixed at body 

R_start 
Type: Orientation Description: Orientation object from world frame to frame_a at initial time 


world 
Type: World 

cylinder 
Type: Shape 

sphere 
Type: Shape 
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