非完整系统的Hamilton化与变分反问题
Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations
摘要：
我们介绍了一种方法，它允许一个恢复一类非完整系统的运动方程，而不是找到一个无约束的哈密顿系统的全相空间，并限制所得到的正则方程相空间的一个适当的子流形。我们首先集中在拉格朗日图片的方法，推导出相应的哈密顿量从勒让德变换。我们用几个例子说明了该方法，我们讨论了它的关系庞特里亚金最大值原理。
英文摘要：
We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations to an appropriate submanifold of phase space. We focus first on the Lagrangian picture of the method and deduce the corresponding Hamiltonian from the Legendre transformation. We illustrate the method with several examples and we discuss its relationship to the Pontryagin maximum principle.
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