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给出构造Hamilton系统的准正则变换的方法,首先将Hamilton系统变换成Birkhoff系统,然后将Birkhoff系统作规范变换并实现Hamilton化. 指出对一个Hamilton系统存在多种准正则变换. 举例说明所得结果的应用.
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关键词:
- Hamilton系统 /
- 准正则变换 /
- Birkhoff系统 /
- 规范变换
A method of constructing canonoid transformations with respect to a Hamiltonian is presented. First, the Hamiltonian system is transformed into a Birkhoffian system. Second, the Birkhoffian system is transformed into a new one under gauge transformation. Finally, the Hamiltonization of new Birkhoffian system is realized. It is pointed out that there exist many different canonoid transformations for one Hamiltonian system. Two examples are given to illustrate the application of the results.[1] Goldstein H, PooleC, Safko J 2002 Classical mechanics, 3nd ed. (Redwood City: Addison-Wesley)
[2] Saletan E J, Cromer A H 1997 Theoretical mechanics (New York: John Wiley)
[3] Santilli R M 1983 Foundations of Theoretical mechanics II (New York: Springer-Verlag)
[4] Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoff system (Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔、 史荣昌、 张永发、 吴惠彬 1996 Birkhoff 系统动力学(北京: 北京理工大学出版社)]
[5] Ding G T 2010 Journal of Dynamics and Control 8 8 (in Chinese)[丁光涛 2010 动力学与控制学报 8 8]
[6] Li Y C, Liang J H, Mei F X 2002 Acta Mechanica Solida Sinica 23 203 (in Chinese)[李元成、 梁景辉、 梅凤翔 2002 固体力学学报 23 203]
[7] Wu H B, Mei F X 2005 Chin. Phys. 14 2391
[8] Mei F X, Wu H B, Zhang Y F 2006 Chin. Phys. 15 1662
[9] Mei F X, Xie J F, Gang T Q 2007 Chin. Phys. 16 2845
[10] Zhang R C,Wang L H,Yue C Q 2007 Acta Phys. Sin. 56 3050 (in Chinese)[张睿超、 王连海、 岳成庆 2007 56 3050]
[11] Lou Z M 2008 Acta Phys. Sin. 57 1307 (in Chinese) [楼智美 2008 57 1307]
[12] Ding G T 2010 Acta Phys.Sin. 59 8326(in Chinese)[丁光涛 2010 59 8326]
[13] Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese )[罗绍凯、 张永发 等 2008 约束系统动力学研究进展 (北京: 科学出版社)]
[14] Ding G T 2009 Acta Phys. Sin. 58 3620 (in Chinese)[丁光涛 2009 58 3620]
[15] Ding G T 2009 Science in China (Series G ) 39 785 (in Chinese)[丁光涛 2009 中国科学(G辑)39 785]
[16] Ding G T 2009 Acta Phys. Sin. 58 6725 (in Chinese)[丁光涛 2009 58 6725]
[17] Ding G T 2009 Acta Phys. Sin. 58 7431 (in Chinese)[丁光涛 2009 58 7431]
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[1] Goldstein H, PooleC, Safko J 2002 Classical mechanics, 3nd ed. (Redwood City: Addison-Wesley)
[2] Saletan E J, Cromer A H 1997 Theoretical mechanics (New York: John Wiley)
[3] Santilli R M 1983 Foundations of Theoretical mechanics II (New York: Springer-Verlag)
[4] Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoff system (Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔、 史荣昌、 张永发、 吴惠彬 1996 Birkhoff 系统动力学(北京: 北京理工大学出版社)]
[5] Ding G T 2010 Journal of Dynamics and Control 8 8 (in Chinese)[丁光涛 2010 动力学与控制学报 8 8]
[6] Li Y C, Liang J H, Mei F X 2002 Acta Mechanica Solida Sinica 23 203 (in Chinese)[李元成、 梁景辉、 梅凤翔 2002 固体力学学报 23 203]
[7] Wu H B, Mei F X 2005 Chin. Phys. 14 2391
[8] Mei F X, Wu H B, Zhang Y F 2006 Chin. Phys. 15 1662
[9] Mei F X, Xie J F, Gang T Q 2007 Chin. Phys. 16 2845
[10] Zhang R C,Wang L H,Yue C Q 2007 Acta Phys. Sin. 56 3050 (in Chinese)[张睿超、 王连海、 岳成庆 2007 56 3050]
[11] Lou Z M 2008 Acta Phys. Sin. 57 1307 (in Chinese) [楼智美 2008 57 1307]
[12] Ding G T 2010 Acta Phys.Sin. 59 8326(in Chinese)[丁光涛 2010 59 8326]
[13] Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese )[罗绍凯、 张永发 等 2008 约束系统动力学研究进展 (北京: 科学出版社)]
[14] Ding G T 2009 Acta Phys. Sin. 58 3620 (in Chinese)[丁光涛 2009 58 3620]
[15] Ding G T 2009 Science in China (Series G ) 39 785 (in Chinese)[丁光涛 2009 中国科学(G辑)39 785]
[16] Ding G T 2009 Acta Phys. Sin. 58 6725 (in Chinese)[丁光涛 2009 58 6725]
[17] Ding G T 2009 Acta Phys. Sin. 58 7431 (in Chinese)[丁光涛 2009 58 7431]
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