Mei Symmetry and New Conserved Quantities of Tzénoff Equations for the Variable Mass Higher-Order Nonholonomic System

Abstract

Operational systems of spacecraft are general variable mass mechanics systems, and their symmetries and conserved quantities imply profound physical rules of the space system. We study the Mei symmetry of Tzénoff equations for a variable mass nonholonomic system and the new conserved quantities derived. The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented. This result has some theoretical values in further research of conservation laws obeyed by the variable mass system.

Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems

“…Mei symmetry (the form invariance) is a new type of symmetry theory proposed by Mei and his collaborators, relating to the form invariance of differential equations under dynamical transformations. [28,29] For the Lagrangian L s,d = L s,d (t,t + , q s , q + s ), the determining equations of Mei symmetry of the discrete Lagrangian systems are…”

“…In the following definitions and theorems, the generators are the conformal invariance of Mei symmetry because the generators' vector (29) is the Mei symmetry firstly. Definition 2 For the discrete perturbed Lagrangian systems (25) and (26), if there exists a nonsingular matrix…”

Symmetries and conserved quantities of constrained mechanical systems

“…see references [36][37][38][39]. There have been some important results on the study of the Lie symmetry of mechanical systems [40][41][42][43][44][45][46][47][48].…”

“…Under the infinitesimal transformations (46), the determining equations of the Lie symmetry of Eq. (26) have the form…”