非保守系统广义Raitzin正则方程的形式不变性与非Noether守恒量

Form invariance and non-Noether conserved quantity of generalized Raitzin's canonical equations of non-conservative system

研究非保守系统广义Raitzin正则方程的形式不变性与非Noether守恒量.列出系统的Raitzin正则方程.提出在无限小变换下系统形式不变性的定义和判据.给出系统的形式不变性是Lie对称性的充要条件.建立Hojman守恒定理,并举例说明结果的应用.

The form invariance and the non-Noether conserved quantity of generalized Raitzin＇ s canonical equations of nonconservative system are studied. The definition and criterion of the form invariance in the system under infinitesimal transformations are proposed. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally, an example is given to illustrate the application of the result.