| Abstract: |
| Given a mechanical system subject to nonholonomic constraints, there are at least the two following ways to determine equations of motion: (1) the generalisation to geometric mechanics of $F=ma$; (2) the extremals of a constrained variational problem. Generally, these two approaches yield different trajectories. The following problem is studied for kinetic energy minus potential energy Lagrangians: when is a given trajectory for approach (1) also a trajectory for approach (2)? Said otherwise: when are physical motions also extremals for a variational problem? Under weak technical assumptions (such as are normally tacitly made whenever this problem is studied), we give necessary and sufficient conditions that can be applied to a given trajectory for approach (1) or to all trajectories for approach (1). |
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