Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

Abstract

Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied. The differential equations of motion of the Appell equation for the system, the definition and criterion of Lie symmetry, the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained. The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained. An example is given to illustrate the application of the results.

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.…”

Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod

“…[9] The symmetry method has been developed as a general method for solving the differential equations of mechanical systems. In addition to Noether symmetry, [9][10][11][12][13][14][15][16][17][18] Lie symmetry for mechanical systems has also been developed, [19][20][21][22][23][24][25][26][27] as well as Mei symmetry (form invariance), [28][29][30][31] unified symmetry, [32,33] conformal invariance, [34][35][36][37] and other symmetries. [38,39] The application of symmetry methods in mechanical systems is referred to several studies.…”

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

“…It is well known that the symmetric method plays a significant role in reducing and constructing exact solutions of nonlinear partial differential equations (NPDEs). [1][2][3][4][5][6] Over the past decades, there have been several methods proposed to seek exact solutions of NPDEs, for example, the nonclassical method, the generalized conditional symmetry (GCS) method, the nonlocal symmetry method, the potential symmetry method, [7][8][9][10] etc. Moreover, much progress has been made in the study on variable separation for NPDEs.…”