Some geometric aspects of variational calculus in constrained mechanics

Details Some geometric aspects of variational calculus in constrained mechanics Some geometric aspects of variational calculus in constrained mechanics

2000-04-13

arxiv.org/abs/math-ph/0004019v1

Physics

Mathematical Physics

LaTex file, 24 pages

Scientific paper

We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of both vakonomic and nonholonomic frameworks are obtained. We study specifically the existence of infinitesimal variations in both cases. When the constraints are integrable, both formalisms are compared and it is proved that they coincide. As examples, we give geometric formulations of the equations of motion for the case of optimal control and for vakonomic and nonholonomic mechanics with constraints linear in the velocities.

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