Abstract
This chapter describes a new rigid body formulation for multibody dynamics, embedded in a natural coordinate framework, and its application as a control input interface for optimal control theory within a direct transcription method. In contrast to the rotationless formulation, see also [3], this scheme exploits the rotational invariance of certain rigid bodies, i.e. rotors, in regard to their mass distribution. This makes possible a separation of the general rigid body movement in a spin part and a complementary rotation part. The resulting equations of motion feature a simple mass matrix with mostly constant entries and without the need of transcendental functions. Furthermore the separated spin coordinate serves as a control input interface within an optimal control problem.
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Acknowledgments
Support for this research was provided by the Deutsche Forschungsgemeinschaft (DFG) under Grant BE 2285/10-1. This support is gratefully acknowledged.
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Becker, C., Betsch, P. (2014). Application of a Gyrostatic Rigid Body Formulation in the Context of a Direct Transcription Method for Optimal Control in Multibody Dynamics . In: Terze, Z. (eds) Multibody Dynamics. Computational Methods in Applied Sciences, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-319-07260-9_10
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DOI: https://doi.org/10.1007/978-3-319-07260-9_10
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