A type of the new exact and approximate conserved quantity deduced from Mei symmetry for a weakly nonholonomic system

Abstract

A type of structural equation, new exact and approximate conserved quantity which are deduced from Mei symmetry of Lagrange equations for a weakly nonholonomic system, are investigated. First, Lagrange equations of weakly nonholonomic system are established. Next, under the infinitesimal transformations of Lie groups, the definition and the criterion of Mei symmetry for Lagrange equations in weakly nonholonomic systems and its first-degree approximate holonomic system are given. And then, the expressions of new structural equation and new exact and approximate conserved quantities of Mei symmetry for Lagrange equations in weakly nonholonomic systems are obtained. Finelly, an example is given to study the question of the exact and the approximate new conserved quantities.

Classification of Second Order Painlevé Type Equations Under the Mei Symmetrical Transformations

“…The non-holonomic system can be used directly to obtain the holonomic system for the differential equation corresponding to motion. Under the Lie group of infinitesimal transformation, for the weak non-holonomic system, Han et al suggested the new Mei symmetries of the exact and approximate nature of the Lagrange equation [9]. The inverse problem of the Mei symmetries of non-holonomic systems with variable mass was proposed by Huang and Cai [10].…”

Classification of Painlevé type equations by the Mei symmetries and their exact solutions

“…The non-holonomic system can be used directly to obtain the holonomic system for the differential equation corresponding to motion. Under the Lie group of infinitesimal transformation, for the weak non-holonomic system, Han et al suggested the new Mei symmetries of the exact and approximate nature of the Lagrange equation [11]. The inverse problem of the Mei symmetries of nonholonomic systems with variable mass was proposed by Huang and Cai [12].…”