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Controllability of rolling bodies with regular surfaces

Moghadasi, S. R ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.4134/JKMS.j140298
  3. Publisher: Korean Mathematical Society
  4. Abstract:
  5. 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
  6. Keywords:
  7. Controllability ; Geodesic curvature ; Isometry group ; Rolling bodies
  8. Source: Journal of the Korean Mathematical Society ; Volume 53, Issue 4 , 2016 , Pages 725-735 ; 03049914 (ISSN)
  9. URL: http://koreascience.or.kr/journal/view.jsp?kj=DBSHBB&py=2016&vnc=v53n4&sp=725