대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권4호
  • /
  • Pages.725-735
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  • 2016
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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CONTROLLABILITY OF ROLLING BODIES WITH REGULAR SURFACES

  • Moghadasi, S. Reza (Department of Mathematical Science Sharif University of Technology)
  • 투고 : 2014.05.14
  • 발행 : 2016.07.01
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초록

A pair of bodies rolling on each other is an interesting example of nonholonomic systems in control theory. There is a geometric condition equivalent to the rolling constraint which enables us to generalize the rolling motions for any two-dimensional Riemannian manifolds. This system has a five-dimensional phase space. In order to study the controllability of the rolling surfaces, we lift the system to a six-dimensional space and show that the lifted system is controllable unless the two surfaces have isometric universal covering spaces. In the non-controllable case there are some three-dimensional orbits each of which corresponds to an isometry of the universal covering spaces.

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참고문헌

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