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| Titel: |
Non-holonomic Euler-Poincare equations and stability in Chaplygin's sphere |
| Auteur: |
Schneider, David |
| Verschenen in: |
Dynamical systems |
| Paginering: | Jaargang 17 (2002) nr. 2 pagina's 87-130 |
| Jaar: |
2002-06-01 |
| Inhoud: |
A method of reducing several classes of non-holonomic mechanical systems that are defined on semidirect products of Lie groups is developed. The method reduces the Lagrange-d'Alembert principle to obtain a reduced constrained principle that determines Euler-Poincare equations on the reduced space. The theory is demonstrated by deriving the reduced equations of motion for several examples of rigid bodies that roll without slipping. Our method of reduction is then used as a framework to obtain several results related to Chaplygin's sphere. The first result determines the stability of the relative equilibria of Chaplygin's sphere: the ball spins stably about the principal axes with the largest and smallest moments of inertia and unstably about the middle axis. The next results use two different approaches to stabilize the rotation of the ball about its middle axis. The first approach controls an internal rotor that has been added to the ball and the second approach controls the plane the ball rolls upon by forces of horizontal translations. We briefly consider the system where the plane is allowed to react to the motion of the ball, stating the equations of motion and identifying the steady rotations. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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