A new type of adiabatic invariants for Birkhoffian system

被引：24

作者：

Zhang Yi ^{[1
]}

机构：

[1] Univ Sci & Technol, Dept Civil Engn, Suzhou 215011, Peoples R China

来源：

ACTA PHYSICA SINICA | 2006年 / 55卷 / 08期

关键词：

Birkhoffian system; Lie symmetry; perturbation; adiabatic invariant;

D O I：

10.7498/aps.55.3833

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The perturbation of symmetries and adiabatic invariants for Birkhoffian system are studied. The exact invariants in the form of Hojman conserved quantities introduced by the Lie symmetries of Birkhoffian system without perturbations are given. Based on the definition of high-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for Birkhoffian system under the action of small disturbance is investigated, and a new type of adiabatic invariants of the system are obtained. An example is given to illustrate the application of the results.

引用

页码：3833 / 3837

页数：5

共 31 条

[1] Birkhoff George D., 1927, Dynamical Systems, V9
[2] Poincare bifurcation in second order autonomous perturbed Birkhoff system
Chen, XW
Mei, FX
[J]. MECHANICS RESEARCH COMMUNICATIONS, 2000, 27 (03) : 365 - 371
[3] Lie symmetries and conserved quantities of relativistic Birkhoff systems
Fu, JL
Wang, XM
[J]. ACTA PHYSICA SINICA, 2000, 49 (06) : 1023 - 1027
[4] GALIULLAN AS, 1989, ANAL DYNAMICS
[5] [郭永新 Guo Yongxin], 2003, [应用数学和力学, Applied Mathematics and Mechanics], V24, P62
[6] Birkhoffian formulations of nonholonomic constrained systems
Guo, YX
Luo, SK
Shang, M
Mei, FX
[J]. REPORTS ON MATHEMATICAL PHYSICS, 2001, 47 (03) : 313 - 322
[7] Luo SK, 2002, CHINESE PHYS LETT, V19, P449, DOI 10.1088/0256-307X/19/4/301
[8] Luo SK, 2001, CHINESE PHYS, V10, P271, DOI 10.1088/1009-1963/10/4/301
[9] Mei F. X., 1999, Application of Lie Group and Lie Algebraic in Constrained Mechanical System
[10] First integral and integral invariant of Birkhoffian system
Mei, FX
Wu, HB
[J]. CHINESE SCIENCE BULLETIN, 2000, 45 (05): : 412 - 414

← 1 2 3 4 →