Chetaev型约束力学系统Appell方程的Lie对称性与守恒量

Lie symmetry and conserved quantity of Appell equation for a Chetaev’s type constrained mechanical system

研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用.

Lie symmetry of Appell equation and conserved quantity deduced directly by Lie symmetry for a Chetaev’s type constrained mechanical system are investigated.The relations between Lagrange function and A function are analyzed.A general approach of studying conserved quantity deduced by Lie symmetry of Appell equation for a Chetaev’s type constrained mechanical system is discussed.The definition and the criterion of Lie symmetry of Appell equations under the infinitesimal transformations of groups are given.The structural equation of Lie symmetry and the expression of conserved quantity deduced directly by Lie symmetry are obtained.An example is given to illustrate the application of the results.