双球面上Lagrange和Hamilton力学的整体表述
Global Formulations of Lagrangian and Hamiltonian Mechanics on Two-Spheres
摘要：
本文给出了在任意数目的两球乘积上演化的拉格朗日变分动力学和哈密顿变分动力学的整体形式。四种类型的欧拉-拉格朗日方程和汉密尔顿方程是在两个球体上以无坐标的方式开发的，而不依赖于可能导致奇异性和繁琐的运动方程的局部参数化。所提出的拉格朗日和哈密顿动力学的内禀公式是新颖的，因为它们结合了两个球的几何形状，从而产生了表示为compensable的运动方程，并且它们在分析和计算全局动力学中是有用的。
英文摘要：
This paper provides global formulations of Lagrangian and Hamiltonian variational dynamics evolving on the product of an arbitrary number of two-spheres. Four types of Euler-Lagrange equations and Hamilton's equations are developed in a coordinate-free fashion on two-spheres, without relying on local parameterizations that may lead to singularities and cumbersome equations of motion. The proposed intrinsic formulations of Lagrangian and Hamiltonian dynamics are novel in that they incorporate the geometry of two-spheres, resulting in equations of motion that are expressed compactly, and they are useful in analysis and computation of the global dynamics.
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