Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems

doi:10.1088/1674-1056/28/3/030201

Abstract

We investigate the perturbation to discrete conformal invariance and the adiabatic invariants of Lagrangian systems. A variational algorithm is proposed for a system subjected to the perturbation quantities. The discrete determining equations of the perturbations to conformal invariance are established. For perturbed Lagrangian systems, the condition of the existence of adiabatic invariant is derived from the discrete perturbation to conformal invariance. The numerical simulations demonstrate that the variational algorithm has the higher precision and the longer time stability than the standard numerical method.

Keywords: variational integrator discrete perturbation to conformal invariance discrete adiabatic invariants disturbed Lagrangian systems

Received: 31 October 2018
Revised: 05 December 2018
Accepted manuscript online:

PACS:	02.20.Sv	(Lie algebras of Lie groups)
	46.15.Ff	(Perturbation and complex analysis methods)
	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	11.30.-j	(Symmetry and conservation laws)

Fund:

Project supported by the National Natural Science Foundation of China (Grant No. 11502071) and the Special Research Project of Beijing Information Science and Technology University, China.

Corresponding Authors: Li-Qun Chen
E-mail: chenliqun@hit.edu.cn

Cite this article:

Li-Li Xia(夏丽莉), Xin-Sheng Ge(戈新生), Li-Qun Chen(陈立群) Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems 2019 Chin. Phys. B 28 030201

[1]	Burgers J M 1917 Annalen der Physik 52 195
[2]	Baikov V A, Gazizov R K and Ibragimov N H 1988 Mat. Sb. 178 435 (English Transl. in Math. USSR Sb. 64 (1989) 427)
[3]	Karczewska A, Rozmej P, Infeld E and Rowlands G 2017 Phys. Lett. A 381 270
[4]	Kruskal M 1962 J. Math. Phys. 3 806
[5]	Helander P, Lisak M and Semenov V E 1992 Phys. Rev. Lett. 68 3659
[6]	Pritula G M, Petrenko E V and Usatenko O V 2018 Phys. Lett. A 382 548
[7]	Djukić Dj S 1981 Internat. J. Non-Linear Mech. 16 489
[8]	Cveticanin L 1994 Internat. J. Non-Linear Mech. 29 799
[9]	Noether A E 1918 Nachr. Akad. Math. 2 235
[10]	Zhao Y Y and Mei F X 1996 Acta. Mech. Sin. 28 207
[11]	Paliathanasis A and Jamal S 2018 J. Geom. Phys. 124 300
[12]	Wang P 2012 Nonlinear Dyn. 68 53
[13]	Chen X W, Li Y M and Zhao Y H 2005 Phys. Lett. A 337 274
[14]	Luo S K, Cai J L and Jia L Q 2008 Chin. Phys. B 17 3542
[15]	Zhang M J, Fang J H and Lu K 2010 Int. J. Theor. Phys. 49 427
[16]	Yang M J and Luo S K 2018 Internat. J. Non-Linear Mech. 101 16
[17]	Galiullin A S, Gafarov G G, Malaishka R P and Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN)
[18]	Mei F X, Xie J F and Gang T Q 2008 Acta Mech. Sin. 24 583
[19]	Cai J L, Luo S K and Mei F X 2008 Chin. Phys. B 17 3170
[20]	Karevski D and Schütz G M 2017 Phys. Rev. Lett. 118 030601
[21]	Wang P Commun. Nonlinear Sci. 59 463
[22]	Logan J D 1973 Aequat. Math. 9 210
[23]	Levi D, Martina L and Winternitz P 2015 J. Phys. A-Math. Theor. 48 025204
[24]	Lutzky M 1998 Internat. J. Non-Linear Mech. 33 393
[25]	Zhang M J 2012 Acta Mech. 223 679
[26]	Dorodnitsyn V 2001 Appl. Numer. Math. 39 307
[27]	Xia L L and Chen L Q 2013 Acta Mech. 224 2037
[28]	Mei F X 2000 J. Beijing Inst. Technol. 9 120
[29]	Zheng S W, Wang J B, Chen X W and Xie J F 2012 Chin. Phys. Lett. 29 20201
[30]	Dorodnitsyn V 1993 Dokl. Akad. Nauk. 328 678
[31]	Marsden J E and West M 2001 Acta Numer. 10 357
[32]	Sharma H, Patil M and Woolsey C 2018 Commun. Nonlinear Sci. 64 159

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Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems

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