相空间中相对运动完整力学系统的共形不变性与守恒量

Conformal invariance and conserved quantity of relative motion holonomic dynamical system in phase space

研究了相空间中相对运动完整力学系统的共形不变性与守恒量.给出了该系统共形不变性的定义,并推导出相空间中相对运动完整力学系统的运动微分方程具有共形不变性并且是Lie对称性的充分必要条件.利用规范函数满足的结构方程导出该系统相应的守恒量,并给出应用算例.

Conformal invariance and conserved quantity of relative motion holonomic dynamical system in phase space are studied. The definition of conformal invariance of relative motion holonomic dynamical system in phase space is provided. The necessary and sufficient conditions that conformal invariance of the system would be Lie symmetry are deduced. By use of a structure equation that the gauge function satisfies, the corresponding conserved quantity of the system is derived. Finally an illustrative example is given to verify the results.