Mei conserved quantity directly induced by Lie symmetry in a nonconservative Hamilton system

Abstract

In this paper, we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented. The condition under which the Lie symmetry of the system directly induces the Mei conserved quantity is given. Meanwhile, an example is discussed to illustrate the application of the results. The present results have shown that the Lie symmetry of a nonconservative Hamilton system can also induce the Mei conserved quantity directly.

Lie Reduction and Conditional Symmetries of Some Variable Coefficient Nonlinear Wave Equations

“…which corresponds to a subcase of case 6 of Table 1 in Ref. [13], where q = 0. Its Lie invariance algebra is generated by the operators…”

“…Let us consider Lie reduction of subcase of case 5 of Table 1 in Ref. [13], the corresponding equation is…”

“…Using this and the second additional equivalence transformations in Table 1 of Ref. [13], i.e. t = t, x = x −1 , ũ = x 3 u, we can obtain exact solutions of Eq.…”

“…where H u = 0, was investigated with the symmetry point of view. [13] Here H and k are arbitrary functions of their argument, t is the time coordinate and x is the one-space coordinate. In that paper, a complete group classifications of the whole class (1) were performed.…”

Accurate conserved quantity and approximate conserved quantity deduced from Noether symmetry for a weakly Chetaev nonholonomic system

“…Since then, the symmetry of mechanical system with constraints and the theory of conservation were rapidly developed and the fruitful results have been achieved [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Scholars have made some achievements for nonholonomic mechanical system which is one research direction of mechanical system with constraints [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Besides, there is a special nonholonomic mechanical system in which a small parameter is contained in constraint equation, which has a small difference from the holonomic system and is defined as the weakly nonholonomic system.…”