The falling cat as a port-controlled Hamiltonian system

Authors

Abstract

In this article, the falling cat is modeled as two jointed axial symmetric cylinders with arbitrary twist under the constraint of the vanishing total angular momentum. As a control system with the constraint taken into account, this model is formulated as a port-controlled Hamiltonian system defined on the cotangent bundle of the shape space for the jointed cylinders. A control is then designed as a function on the cotangent bundle, according to a standard procedure. Thus, the equations of motion are determined on the cotangent bundle together with the control. The whole motion as a vibrational motion of the falling cat is obtained after integrating the constraint equation of the vanishing total angular momentum. An example of the falling cat is given in which the model turns a somersault to approach a target state in equilibrium with an expected rotation after finishing a vibrational motion.

Keywords

Geometric mechanics; Port-controlled Hamiltonian systems; The falling cat

Citation

Journal: Journal of Geometry and Physics
Year: 2012
Volume: 62
Issue: 2
Pages: 279–291
Publisher: Elsevier BV
DOI: 10.1016/j.geomphys.2011.10.018

BibTeX

@article{Iwai_2012,
  title={{The falling cat as a port-controlled Hamiltonian system}},
  volume={62},
  ISSN={0393-0440},
  DOI={10.1016/j.geomphys.2011.10.018},
  number={2},
  journal={Journal of Geometry and Physics},
  publisher={Elsevier BV},
  author={Iwai, Toshihiro and Matsunaka, Hiroki},
  year={2012},
  pages={279--291}
}

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References

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