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

作　　者：李媛媛 张绍成[3] 花巍 刘畅[1,2] 刘世兴[1,2] 郭永新[1,2] Li Yuanyuan;Zhang Shaocheng;Hua Wei;Liu Chang;Liu Shixing;Guo Yongxin(College of Physics,Liaoning University,110036,China;Institute of Space Science and Technology,Liaoning University,110036,China;Informatization Center,Liaoning University,Shenyang 110036,China;College of Physics Science and Technology,Shenyang Normal University,Shenyang 110036,China)

机构地区：[1]辽宁大学物理学院,沈阳110036 [2]辽宁大学空间科学与技术研究院,沈阳110036 [3]辽宁大学信息化中心,沈阳110036 [4]沈阳师范大学物理科学与技术学院,沈阳110036

出　　处：《动力学与控制学报》2022年第1期1-7,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11872030,11972177,11772144);辽宁省教育厅自然科学项目(LJC202003)。

摘　　要：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.

关 键 词：幂律Hamilton原理 非线性动力学 幂律Hamilton方程 控制参数 

分 类 号：O316[理学—一般力学与力学基础]