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引入Whittaker方程的Birkhoff表示,构造与该表示对应的Hamilton函数,并利用Hamilton-Poisson方法得到Whittaker方程的解.指出上述Hamilton函数与传统分析力学中Hamilton函数的区别.
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关键词:
- Whittaker方程 /
- Hamilton化 /
- Birkhoff表示 /
- 分析力学逆问题
A Birkhoffian representation of Whittaker equations is introduced. A Hamiltonian corresponding to the Birkhoffian representation is constructed. The Whittaker equations are solved by using the Hamilton-Poisson method. The difference between the above Hamiltonian and the Hamiltonians of traditional analytical mechanics is pointed.-
Keywords:
- Whittaker equations /
- Hamiltonization /
- Birkhoffian representation /
- inverse problem of analytical mechanics
[1] Goldstein H, Poole C, Safko J 2002 Classical Mechanics (3rd ed) (Redwood City: Addison-Wesley)
[2] (in Chinese)[张睿超、 王连海、 岳成庆 2007 56 3050]
[3] Santillli R M 1978 Foundations of Theoretical Mechanics (Ⅰ) (New York: Springer-Verlag)
[4] Mei F X, Xie J F, Gang T Q 2007 Chin. Phys. 16 2845
[5] Riewe F 1997 Phys. Rev. E 55 3581
[6] Ge W K 2006 Acta Phys. Sin. 55 10 (in Chinese)[葛伟宽 2006 55 10]
[7] Guo Y X, Mei F X, Shang M 2007 Chin. Phys. 16 292
[8] Zhang R C, Wang L H, Yue C Q 2007 Acta Phys. Sin. 56 3050
[9] Ding G T 2008 Acta Phys. Sin. 57 7415 (in Chinese) [丁光涛 2008 57 7415]
[10] Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian 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)]
[11] Ding G T 2010 J. Dynam. Contr. 8 8 (in Chinese) [丁光涛 2010 动力学与控制学报 8 8]
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[1] Goldstein H, Poole C, Safko J 2002 Classical Mechanics (3rd ed) (Redwood City: Addison-Wesley)
[2] (in Chinese)[张睿超、 王连海、 岳成庆 2007 56 3050]
[3] Santillli R M 1978 Foundations of Theoretical Mechanics (Ⅰ) (New York: Springer-Verlag)
[4] Mei F X, Xie J F, Gang T Q 2007 Chin. Phys. 16 2845
[5] Riewe F 1997 Phys. Rev. E 55 3581
[6] Ge W K 2006 Acta Phys. Sin. 55 10 (in Chinese)[葛伟宽 2006 55 10]
[7] Guo Y X, Mei F X, Shang M 2007 Chin. Phys. 16 292
[8] Zhang R C, Wang L H, Yue C Q 2007 Acta Phys. Sin. 56 3050
[9] Ding G T 2008 Acta Phys. Sin. 57 7415 (in Chinese) [丁光涛 2008 57 7415]
[10] Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian 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)]
[11] Ding G T 2010 J. Dynam. Contr. 8 8 (in Chinese) [丁光涛 2010 动力学与控制学报 8 8]
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