一类二阶非标准广义力学的正则变换和第一积分  

Canonical Transformations and First Integrals of a Class of Second-Order Non-Standard Generalized Mechanics

作　　者：朱琳 张毅[2] Zhu Lin;Zhang Yi(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)

机构地区：[1]苏州科技大学数学科学学院,苏州215009 [2]苏州科技大学土木工程学院,苏州215011

出　　处：《动力学与控制学报》2024年第4期16-22,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12272248,11972241)。

摘　　要：研究带有指数Lagrange函数的二阶非标准广义力学的正则变换以及关于第一积分的Poisson理论.首先,建立二阶非标准广义力学的Hamilton原理,导出Euler-Lagrange方程,并由Legendre变换定义Hamilton函数,建立正则方程;其次,建立二阶非标准广义力学的正则变换的判别条件,并通过母函数的不同选择给出四种基本形式的正则变换;最后,验证二阶非标准广义力学具有Lie代数结构,建立关于第一积分的Poisson理论.文中通过算例演示结果之应用.In this paper,we studied the canonical transformations of second-order non-standard generalized mechanics with exponential Lagrangians and Poisson theory on the first integrals.First,Hamilton principle of second-order nonstandard generalized mechanics is established,the Euler-Lagrange equations are derived,the Hamiltonian is defined by using Legendre transformation,and the canonical equation are established.Secondly,the discriminant conditions of canonical transformation of second-order nonstandard generalized mechanics are established,and four basic forms of canonical transformation are given by different choices of generating functions.Finally,the Lie algebraic structure of second-order non-standard generalized mechanics is verified,and Poisson theory of the first integral is established.Some examples are given to demonstrate the application of the results.

关 键 词：广义力学 非标准Lagrange函数 正则变换 Poisson理论 

分 类 号：O316[理学—一般力学与力学基础]