Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T02:32:08.238Z Has data issue: false hasContentIssue false
  • English
  • Français

Rolling of a body on a plane or a sphere: a geometric point of view

Published online by Cambridge University Press:  17 April 2009

S. Reza Moghadasi
S. Reza Moghadasi
Affiliation:
Department of Mathematics, Sharif Unviersity of Technology, P.O. Box 11365–9415, Tehran, Iran e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A pair of bodies rolling on each other is an interesting example of nonholonomic systems in control theory. Here the controllability of rolling bodies is investigated with a global approach. By using simple geometric facts, this problem has been completely solved in the special case where one of them is a plane or a sphere.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 245 - 256
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Agrachev, A.A. and Sachkov, Yu.L., ‘An intrinsic approach to the control of rolling bodies’, Proc. 38th IEEE Conf. on Decision and Control 1 (1999), 431–435.Google Scholar
[2]do Carmo, M.P., Differential geometry of curves and surfases, (Translated from the Portuguese) (Prentice-Hall Inc., Englewood Cliffs, N.J., 1976).Google Scholar
[3]Goto, M., ‘On an arcwise connected subgroup of a Lie group’, Proc. Amer. Math. Soc. 20 (1969), 157–162.CrossRefGoogle Scholar
[4]Klingenberg, W., A course in differential geometry, Graduate Texts in Mathematics 51, (Translated from the German by Hoffman, David) (Springer-Verlag, New York, 1978).CrossRefGoogle Scholar
[5]Levi, M., ‘Geometric phases in the motion of rigid Bodeis’, Arch. Rational Mech. Anal. 122 (1993), 213–229.CrossRefGoogle Scholar
[6]Li, Z. and Canny, J., ‘Motion of Two Rigid Bodies with Rolling Constraint’, IEEE Trans. Robot. Autom. 6 (1990), 62–72.CrossRefGoogle Scholar
[7]Marigo, A. and Bicchi, A., ‘Rolling Bodies with regular surfases: Controllability theory and aplications’, IEEE Trans. Automat. Control 45 (2000), 1586–1599.CrossRefGoogle Scholar
[8]Montanna, D.J., ‘The kinematics of contact and grasp’, Internat. J. Robotics Res. 7 (1988), 17–32.CrossRefGoogle Scholar