Special Lie symmetry and Hojman conserved quantity of Appell equations for a Chetaev nonholonomic system

Yuelin Han,Xiaoxiao Wang,Liqun Jia,Meiling Zhang

doi:10.1007/s11071-013-0791-1

Abstract

A special Lie symmetry and Hojman conserved quantity of the Appell equations for a Chetaev nonholonomic system are studied. The differential equations of motion and Appell equations of the Chetaev nonholonomic system are established. Under the special Lie symmetry group transformations in which the time is invariable, the determining equation of the special Lie symmetry of the Appell equations for a Chetaev nonholonomic system is given, and the expression of the Hojman conserved quantity is deduced directly from the Lie symmetry. Finally, an example is given to illustrate the application of the results.

Highlights

Appell equations are very important equations in analytical mechanics, and belong to one of the three types of mechanical system in the theory of analytical mechanics [1]
2000, Chinese scholars have made some achievements in the studies of symmetry for mechanical system with constraints [9–24], especially in Lie symmetry’s research [25–39]
This paper works on special Lie symmetry and Hojman conserved quantity of Appell equations for a Chetaev type nonholonomic system

Summary

Introduction

Appell equations are very important equations in analytical mechanics, and belong to one of the three types of mechanical system in the theory of analytical mechanics [1]. 20 years, Chinese scholars have gained fruitful achievements in research, promotion and application of the Appell equation [2–8]. To solve Appell equations, Mei Feng-Xiang, the famous classical mechanics expert, first gained the Noether conserved quantity deduced indirectly from the Noether symmetry by Mei symmetry [40]; Ref. [4] obtained the conserved quantity of Appell equations for the rotational relativistic holonomic system deduced indirectly from the Noether symmetry and Lie symmetry by Mei symmetry; Ref. [42] used Appell to express the structure equation of Mei symmetry and Mei conserved quantity for a non-Chetaev’s type constrained mechanical system. There are fewer research results of Lie symmetry of Appell equations. This paper works on special Lie symmetry and Hojman conserved quantity of Appell equations for a Chetaev type nonholonomic system

Appell equations for a Chetaev nonholonomic system

Determining equation and definition of Lie symmetry

Hojman conserved quantity deduced from the Lie symmetry

An illustrative example

Conclusion