非完整相对运动动力学系统的Lagrange对称性与守恒量

Lagrange symmetries and conserved quantities for the nonholonomic mechanical system in relative motion

研究非完整相对运动动力学系统的Lagrange对称性,给出非完整相对运动动力学系统的Lagrange对称性的定义和判据,并得到非完整相对运动动力学系统的Lagrange对称性导致守恒量的条件和形式.通过算例说明结果的应用.

This paper researchs the Lagrange symmetries and conserved quantities for the nonholonomic mechanical system in relative motion.The definition and criterion of Lagrange symmetry of the systems are given.Theconditions under which a Lagrangesymmetry can lead to a new conserved quantity （ first integral） are obtained and the form of thenew conserved quantity（ first integral） is presented.The example is given to illustrate the application of the results.