期刊论文

Huang Wei-Li

中文

物理学报

1000-3290

2015

64

17

170202-1-170202-6

10.7498/aps.64.170202

(10932002):国家自然科学基金 (批准号:LY12A02008)资助的课题.* Project supported by the National Natural Science Foundation of China(Grant 10932002):浙江省自然科学基金 (Grant LY12A02008):the Natural Science Foundation of Zhejiang Province of China

本校为第一且通讯机构

动力学逆问题是星际航行学、火箭动力学、规划运动学理论的基本问题。 Mei对称性是力学系统的动力学函数在群的无限小变换下仍然满足系统原来的运动微分方程的一种新的不变性。本文研究广义坐标下一般完整系统的Mei对称性以及与Mei对称性相关的动力学逆问题。首先,给出系统动力学正问题的提法和解法。引入时间和广义坐标的无限小单参数变换群,得到无限小生成元向量及其一次扩展。讨论由n个广义坐标确定的一般完整力学系统的运动微分方程,将其Lagrange函数和非势广义力作无限小变换,给出系统运动微分方程的Mei对称性定义,在忽略无限小变换的高阶小量的情况下得到Mei对称性的确定方程,借助规范函数...

Inverse problems in dynamics are the basic problems in astronautics, rocket dynamics, and motion planning theory, etc. Mei symmetry is a kind of new symmetry where the dynamical function in differential equations of motion still satisfies the equation's primary form under infinitesimal transformations of the group. Mei symmetry and its inverse problem of dynamics for a general holonomic system in generalized coordinates are studied. Firstly, the direct problem of dynamics of the system is proposed and solved. Introducing a one-parameter infinitesimal transformation group with respect to time a...