动力学拉格朗日形式与哈密顿形式中动能偏导数的关系
Relation Between the Partial Derivatives of the Kinetic Energy in the Lagrangian and Hamiltonian Formalisms of Dynamics
摘要：
拉格朗日形式主义中动力系统的动能对广义坐标的偏导数不等于哈密顿形式主义中动能对同一坐标的导数，而是相差一个符号。在保守系统的情况下，我们发现了两个偏导数之间的另一个精确关系。我们还确定了另一种形式的动能，其偏导数相对于广义坐标完全消失。
英文摘要：
The partial derivative of the kinetic energy of a dynamical system with respect to a generalized coordinate as it appears in the Lagrangian formalism is not equal to the derivative of the kinetic energy with respect to the same coordinate in the Hamiltonian formalism but differs by a sign. We find another exact relation between the two partial derivatives in the case of a conservative system. We also identify another form of kinetic energy whose partial derivative with respect to a generalized coordinate vanishes identically.
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