Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

Abstract

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied. The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given. The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained. Finally, an example is given to illustrate the application of the results.

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

“…Research of symmetries and conserved quantities of constrained dynamical systems plays an important role in modern mechanical and mathematical sciences, and it is also a developing direction of modern mathematics, mechanics and physics [1][2][3]. Fruitful achievements have been gained in looking for conserved quantities by means of Noether symmetry, Lie symmetry and Mei symmetry [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Theories of the conformal invariance are classified into the gauge field theories in 1960s and 1970s, particularly are a hot topic of gravitational gauge field [22,23].…”