Exact invariants and adiabatic invariants of dynamical system of relative motion

doi:10.1088/1009-1963/13/12/005

中国物理B ›› 2004, Vol. 13 ›› Issue (12): 2003-2007.doi: 10.1088/1009-1963/13/12/005

Exact invariants and adiabatic invariants of dynamical system of relative motion

陈向炜, 王新民, 王明泉

Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China

收稿日期:2004-02-25 修回日期:2004-05-13 出版日期:2005-03-17 发布日期:2005-03-17
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10372053); the Natural Science Foundation of Henan Province, China (Grant No 0311010900), and the Foundation of Young Key Member of the Teachers in Institutions of Higher Lear

Exact invariants and adiabatic invariants of dynamical system of relative motion

Chen Xiang-Wei (陈向炜), Wang Xin-Min (王新民), Wang Ming-Quan (王明泉)

Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China

Received:2004-02-25 Revised:2004-05-13 Online:2005-03-17 Published:2005-03-17
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10372053); the Natural Science Foundation of Henan Province, China (Grant No 0311010900), and the Foundation of Young Key Member of the Teachers in Institutions of Higher Lear

摘要/Abstract

摘要： Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of a dynamical system of relative motion are studied. The perturbation to symmetries for the dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.

Abstract: Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of a dynamical system of relative motion are studied. The perturbation to symmetries for the dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.

Key words: dynamical system of relative motion, perturbation, exact invariant, adiabatic invariant

中图分类号: (General theory of classical mechanics of discrete systems)

45.05.+x

45.30.+s (General linear dynamical systems) 02.30.Zz (Inverse problems)

陈向炜, 王新民, 王明泉. Exact invariants and adiabatic invariants of dynamical system of relative motion[J]. 中国物理B, 2004, 13(12): 2003-2007.

Chen Xiang-Wei (陈向炜), Wang Xin-Min (王新民), Wang Ming-Quan (王明泉). Exact invariants and adiabatic invariants of dynamical system of relative motion[J]. Chinese Physics, 2004, 13(12): 2003-2007.

[1]	叶建春, 李俊, 陈晓红, 黄素梅, 欧阳威. Enhancement of corona discharge induced wind generation with carbon nanotube and titanium dioxide decoration[J]. 中国物理B, 2019, 28(9): 95202-095202.
[2]	宋宗斌, 杨雪滢, 封文星, 席忠红, 李烈娟, 石玉仁. Decaying solitary waves propagating in one-dimensional damped granular chain[J]. 中国物理B, 2018, 27(7): 74501-074501.
[3]	王扶刚, 杨阳阳, 韩娟芳, 段文山. Head-on collision between two solitary waves in a one-dimensional bead chain[J]. 中国物理B, 2018, 27(4): 44501-044501.
[4]	杜文青, 孙建安, 杨阳阳, 段文山. Envelope solitary waves and their reflection and transmission due to impurities in a granular material[J]. 中国物理B, 2018, 27(1): 14501-014501.
[5]	崔金超, 刘世兴, 宋端. A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems[J]. 中国物理B, 2013, 22(10): 104501-104501.
[6]	赵纲领, 陈立群, 傅景礼, 洪方昱. Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices[J]. 中国物理B, 2013, 22(3): 30201-030201.
[7]	张伟伟, 方建会 . Noether–Mei symmetry of discrete mechanico-electrical system[J]. 中国物理B, 2012, 21(11): 110201-110201.
[8]	张克军, 方建会, 李燕. Perturbation to Mei symmetry and Mei adiabatic invariants for discrete generalized Birkhoffian system[J]. 中国物理B, 2011, 20(5): 54501-054501.
[9]	董文山, 黄宝歆, 方建会. Noether's theory of generalized linear nonholonomic mechanical systems[J]. 中国物理B, 2011, 20(1): 10204-010204.
[10]	王苍龙, 段文山, 陈建敏, 石玉仁. Anisotropic character of atoms in a two-dimensional Frenkel–Kontorova model[J]. 中国物理B, 2011, 20(1): 14601-014601.
[11]	陶司兴, 夏铁成. The super-classical-Boussinesq hierarchy and its super-Hamiltonian structure[J]. 中国物理B, 2010, 19(7): 70202-070202.
[12]	张毅. Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space[J]. 中国物理B, 2009, 18(11): 4636-4642.
[13]	李元成, 夏丽莉, 王小明. Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems[J]. 中国物理B, 2009, 18(11): 4643-4649.
[14]	张明江, 方建会, 路凯, 张克军, 李燕. Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems[J]. 中国物理B, 2009, 18(11): 4650-4656.
[15]	傅景礼, 聂宁明, 黄健飞, Jimé nez Salvador, 唐贻发, Vá zquez Luis, 赵维加. Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices[J]. 中国物理B, 2009, 18(7): 2634-2641.

Exact invariants and adiabatic invariants of dynamical system of relative motion

Exact invariants and adiabatic invariants of dynamical system of relative motion

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0