Conformal Invariance and Conserved Quantity of Mei Symmetry for Appell Equations in a Holonomic System with Mass Variable

Abstract

For a holonomic system with variable mass, the conformal invariance and the conserved quantity of Mei symmetry of Appell equations are investigated. First, by the infinitesimal one-parameter transformation group and the infinitesimal generator vector, the Mei symmetry and the conformal invariance of differential equations of motion for Appell equations in a holonomic system with variable mass are defined, and the determining equation of Mei symmetry and conformal invariance for Appell equations in a holonomic system with variable mass are given. Then, the Mei-conserved quantity corresponding to the system is derived by means of the structure equation to which the gauge function satisfies. Finally, an example is given to illustrate the application of the result.

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

“…In the 1970s, the mechanics community gradually realized its scientific value. 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].…”

Conformal invariance and conserved quantity of Mei symmetry for Appell equations in a nonholonomic system of Chetaev’s type

“…In 1997, Galiullin et al had proposed concepts of conformal invariance and conformal factor of Birkhoff equations in the study of dynamics in Birkhoffian systems [23], and discussed the relationships between the invariance and the conformal invariance, Lie symmetry and the conformal invariance under the infinitesimal transformations of Pfaff action. Since entering the twenty-first century, Chinese scholars have carried out certain new researches and have gained some achievements in the study of symmetries and conserved quantities for mechanical systems by means of theories of the conformal invariance [24][25][26][27][28][29][30][31][32][33][34][35]. However, for a long time, there are fewer results to Appell equations.…”

“…Reference [34] studied the conformal invariance and conserved quantity of Mei symmetry of Lagrange equations in nonholonomic systems of Chetaev's type. Reference [35] studied the conformal invariance and conserved quantity of Mei symmetry of Appell equations in holonomic systems. This paper will examine conformal invariance and Mei-conserved quantity of Mei symmetry of Appell equations in nonholonomic systems of Chetaev's type.…”