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Rigid Body Kinematics Package

Hanspeter Schaub
Organization: Texas A&M University
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A Mathematica package is presented which provides many commonly used functions in rigid body kinematics. Transformations between the direction cosine matrix, Euler parameters, Gibbs vector, modified Rodrigues parameters, principal rotation vector and the 12 sets of Euler angles are provided. Whenever possible, direct analytical transformations between these sets are used to provide computationally efficient code. Furthermore, the ability to perform two successive rotations and compute the resulting overall attitude vector is provided for each attitude coordinate choice. Similarly, the toolbox allows for the relative attitude vector between two given attitude vectors to be computed. Finally, subroutines are provided that compute the matrix relating the attitude parameter rates to the body angular velocity vector, along with the analytic inverse of this matrix. With these routines the attitude vector time derivative is computed for a given body angular velocity vector.

*Engineering > Mechanical and Structural Engineering

rigid body kinematics, transformations, direction cosine matrix, Euler parameters, Gibbs vector, Rodrigues parameters, principal rotation vecto, attitude vector, angular velocity vector
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RBKtutorial.nb (49.6 KB) - Mathematica notebook
RigidBodyKinematics.m (62.5 KB) - Mathematica package