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.

• Periodical: Applied Mechanics and Materials (Volumes 670-671)
• Pages: 617-625
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.670-671.617
• Online since: October 2014
• Authors: Yao Yu Zhang*, Xian Ting Sun, Xi Chang Xue, Li Qun Jia
• Keywords: Appell Equation, Conformal Invariance, Mei-Conserved Quantity, Variable Mass Holonomic System

References

[1] Noether A E, Invariante variations probleme, Nachr. Akad. Wiss G. ttingen Math. 2(1918) 235.

[2] Zhang,Y., Mei, F.X., Effects of constraints on Noether symmetries and conserved quantities in a Birkhoffian system, J. Acta Phys. Sin, 53(8) (2004) 2419-2423.

DOI: 10.7498/aps.53.2419

[3] Cui J.C., Zhang Y.Y., Jia L.Q., Mei conserved quantity of the Nielsen equation for a non-Chetaev-type non-holonomic system, J. Chin. Phys. 18 (2009)1731-1737.

DOI: 10.1088/1674-1056/18/5/003

[4] Zheng S.W., Xie J.F., Chen X.W. , Another kind of conserved quantity induced directly from Mei symmetry of Tzénoff equations for holonomic systems, J. Acta Phys. Sin. 59 (2010) 5209-5212.

DOI: 10.7498/aps.59.5209

[5] Luo S.K., Li, Z.J., Li,L., A new Lie symmetrical method of finding conserved quantity for dynamical system in phase space, J. Acta Mechanica, 223(12) (2012) 2621–2632.

DOI: 10.1007/s00707-012-0729-6

[6] Li,Z.J., Jiang W.A., Luo S.K., Lie symmetries, symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems, J. Nonlinear Dyn. 67(2012) 445-455.

DOI: 10.1007/s11071-011-9993-6

[7] Luo S.K., Li,Z.J., Li,L., A new Lie symmetrical method of finding conserved quantity for dynamical system in phase space, J. Acta Mech. 223 (2012) 2621-2632.

DOI: 10.1007/s00707-012-0729-6

[8] Jia L.Q., Sun X.T., Zhang M.L., Zhang Y.Y., Han, Y,L., Generalized Hojman conserved quantity deduced from generalized Lie symmetry of Appell equations for a variable mass mechanical system in relative motion, J. Acta Phys. Sin. 63 (2014) 010201.

DOI: 10.7498/aps.63.010201

[9] Ge, M.L., Covariant Lie variation and conformal invariance of Yang-Mills equations and Liouville equation, J. Journal of science, 20(1985) 1538-1540.

[10] Haidari, A.D., Conformal quantum Yang-Mills. J . Math Phys, 27(1986) 2409-2412.

[11] Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M, Analytical Dynamics of Helmholtz, J. Birhoff and Nambu Systems(Moscow: UFN)(in Russian) (1997).

[12] Cai J.L., Conformal invariance of Mei symmetry for a holonomic system with variable mass, J. Chin.J. Phys. 48(6) (2010) 728-735.

[13] Cai J.L., Shi, S.S., Fang, H.J. and Xu, J., Conformal Invariance for the Nonholonomic Constrained Mechanical System of Non-Chetaev's Type, J. Meccanica, 47(1) (2012) 63-69.

DOI: 10.1007/s11012-010-9414-9

[14] Huang W.L., Cai J.L., Conformal invariance and conserved quantity of Mei symmetry for higher-order nonholonomic system, J. Acta Mech. 223(2) (2012) 433-440.

DOI: 10.1007/s00707-011-0573-0

[15] Cai, J.L., Conformal invariance of Mei symmetry for the nonholonomic system of non-Chetaev's type, J. Nonlinear Dynamics, 69(1-2) (2012) 487–493.

DOI: 10.1007/s11071-011-0279-9

[16] Cai J.L., Shi S.S., Conformal invariance and conserved quantity of Mei symmetry for the nonholonomic system of Chetaev's type, J. Acta Phys. Sin. 61(2012) 030201.

DOI: 10.7498/aps.61.030201

[17] Chen X.W., Zhao Y.H., Liu,C., Conformal invariance and conserved quantity for holonomic mechanical systems with variable mass, J. Acta Mech. 58(8) (2009)5150-05.

[18] Cui J.C., Zhang Y.Y., Yang X.F., Jia, L.Q., Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system, J. Chin. Phys. B. 19(3) (2010) 030304.

DOI: 10.1088/1674-1056/19/3/030304

[19] Han Y.L., Sun,X. T, Zhang Y.Y., Jia, L.L., Conformal invariance and conserved quantity of Mei symmetry for Appell equations in holonomic system, J. Acta Phys. Sin. 62 (2013) 160201.

DOI: 10.7498/aps.62.160201