力学系统运动微分方程的对称性与测地偏离

Geodesic Deviation and Symmetries of Differential Equations ofMotion for Mechanical Systems

研究了力学系统运动方程的动力学对称性与伴随对称性的几何性质。结果表明，运动微分方程的对称性为状态流形的拓扑性质，它限定系统沿状态流形上的测地线运动并确定其测地偏离性质。

The geometical properties of dynamical symmetry and adjoint symmetry of equations of motion for mechanical systems are studied The result indicates that the symmetries of differential equations of motion are topological properties of a state manifold which confine the system moving along the geodesics on the state manifold and determine their geodesic deviations