幂律Hamilton方程及其在非线性动力学中的应用

POWER-LAW HAMILTONIAN EQUATIONS AND ITS APPLICATION IN NONLINEAR DYNAMICS

本文对幂律Hamilton作用量应用等时变分法,得到了一种非标准形式的Hamilton方程,这类方程被称之为为幂律Hamilton方程.此方程是用来描述一类特殊动力学系统的运动方程.幂律Hamilton方程中有一个可控参数,通过调整的取值改变物体的运动或动力学系统的轨迹.算例结果表明,幂律Hamilton系统具有不同于标准Hamilton方程的特性,并对其附加特性进行了详细的讨论.

In this paper,a non standard Hamilton equation called the power-law Hamilton equation,is obtained by applying the isochronous variational method to the power-law Hamilton action.These equations are used to describe a special class of dynamical system.There is a controllable parameterγin the power-law Hamiltonian equation.We can change the trajectories of motion of bodies or the behaviors of dynamical systems by adjustingγ.Some examples demonstrate that the power-law Hamiltonian systems have characteristics different from the standard ones,and some additional features are discussed in detail.