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| Exact invariants and adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system | |
| 引用本文： | 乔永芬,李仁杰,孙丹娜. Exact invariants and adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system[J]. 中国物理, 2005, 14(10): 1919-1925 |
| 作者姓名： | 乔永芬 李仁杰 孙丹娜 |
| 作者单位： | Department of Mechanical Engineering and Automation, Zhejiang Institute of Science and Technology, Hangzhou 310018, China;Engineering College of Northeast Agricultural University,Harbin 150030, China;Faculty of Science Laiyang Agricultural College, Laiyang 265200, China;Faculty of Science Laiyang Agricultural College, Laiyang 265200, China;Faculty of Science Laiyang Agricultural College, Laiyang 265200, China |
| 基金项目： | Project supported by the HeilongjiangNatural Science Foundation of China (Grant No 9507). |
| 摘 要： | The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results. |
| 关 键 词： | 非完整系统 Raitzin规范方程 对称性 扰动系统 绝热不变量 |
| 收稿时间： | 2004-11-11 |
| 修稿时间： | 2004-11-112005-05-17 |
Exact invariants and adiabatic invariants of Raitzin''s canonical equations of motion for a nonlinear nonholonomic mechanical system |
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| Qiao Yong-Fen,Li Ren-Jie and Sun Dan-Na. Exact invariants and adiabatic invariants of Raitzin''s canonical equations of motion for a nonlinear nonholonomic mechanical system[J]. Chinese Physics, 2005, 14(10): 1919-1925 | |
| Authors: | Qiao Yong-Fen Li Ren-Jie Sun Dan-Na |
| Affiliation: | Department of Mechanical Engineering and Automation, Zhejiang Institute of Science and Technology, Hangzhou 310018, China;Engineering College of Northeast Agricultural University,Harbin 150030, China;Faculty of Science Laiyang Agricultural College, Laiyang 265200, China; Faculty of Science Laiyang Agricultural College, Laiyang 265200, China |
| Abstract: | The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results. |
| Keywords: | nonholonomic system Raitzin's canonical equation symmetry perturbation exact invariant adiabatic invariant |
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