Special Lie—Mei Symmetry and Conserved Quantities of Appell Equations Expressed by Appell Function

Abstract

Special Lie-Mei symmetry and conserved quantities for Appell equations expressed by Appell functions in a holonomic mechanical system are investigated. On the basis of the Appell equation in a holonomic system, the definition and the criterion of special Lie-Mei symmetry of Appell equations expressed by Appell functions are given. The expressions of the determining equation of special Lie-Mei symmetry of Appell equations expressed by Appell functions, Hojman conserved quantity and Mei conserved quantity deduced from special Lie-Mei symmetry in a holonomic mechanical system are gained. An example is given to illustrate the application of the results.

Lie symmetries, symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems

“…. , n), (25) where, ε is an infinitesimal parameter. Assuming that the disturbed equations (24) are small perturbation on the basis of the undisturbed equations (4), we have the following relation by using (7):…”

“…In 1979, M. Lutzky [11][12][13] applied Lie's theory to the differential equations of motion for the mechanical system, and studied Lie symmetries and conserved quantities of a dynamical system. In the recent 20 years, researchers [2][3][4][5][14][15][16][17][18][19][20][21][22][23][24][25] developed the methods of Noether symmetry and Lie symmetry, and obtained many important results.…”

Lie symmetry and approximate Hojman conserved quantity of Appell equations for a weakly nonholonomic system

“…In the recent 20 years, Chinese researchers have gained fruitful achievements in research, promotion, and application of Appell equations [12][13][14][15][16][17]. Since 2000, Chinese researchers have made some achievements in this research area, especially in Lie symmetry [35][36][37][38][39][40][41][42][43][44][45][46][47] of constrained mechanical systems [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. However, there are fewer results on Appell equations.…”

Dynamical properties of a logistic growth model with cross-correlated noises

“…The associated relaxation time T c and the normalized correlation function C (s) are investigated. The associated relaxation time and the normalized correlation function are usually used to analyze the dynamic properties of a nonlinear stochastic system [18,19].…”