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3D Rigid Body Dynamics

3D Rigid Body Dynamics. 1D translation dynamics:. 3D translation dynamics:. (inertial co-ordinate sys). 1D rotational dynamics:. 3D rotational dynamics:. 3D Rigid Body Dynamics. These products of inertia are constant because the moving co-ordinate system is attached to the rigid body.

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3D Rigid Body Dynamics

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  1. 3D Rigid Body Dynamics 1D translation dynamics: 3D translation dynamics: (inertial co-ordinate sys) 1D rotational dynamics: 3D rotational dynamics:

  2. 3D Rigid Body Dynamics These products of inertia are constant because the moving co-ordinate system is attached to the rigid body for a rectangular mass with the co-ordinate system aligned with the rectangle directions:

  3. 3D Rigid Body Dynamics To calculate the rotation matrix use:

  4. 3D Rigid Body Dynamics Translational dynamics in local body co-ordinate system: Note that the velocity and force are expressed in local coordinates Since the velocity is in local coordinates it must be transformed when integrating the position in global coordinates This form of translational dynamics is popular for vehicle systems since vehicle actuator effects are often more easily expressed in local coordinates

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