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研究带电粒子在磁场中作阻尼运动的分析力学表示. 首先, 求解运动微分方程的Birkhoff力学逆问题, 得到带电粒子的4个Rirkhoff表示; 其次, 导出4个状态空间中Lagrange表示和对应的4个位形空间中Lagrange表示; 第三, 构造出4个Hamilton函数; 最后, 从粒子运动的分析力学表示直接得到4个第一积分, 并求出运动方程的解.
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关键词:
- 约化的Lorentz-Dirac方程 /
- 分析力学表示 /
- 逆问题
The anatylical mechanics representations of a charged particle moving in a uniform magnetic field with radiation friction are studied. First, by solving the inverse problem of Birkhoffian mechanics for the differential equations of motion the 4 Birkhoffian representations of the charged particle are obtained. Secondly, 4 Lagrangian representations in the state space and 4 Lagrangian representations in the configuration space are derived, and then 4 Hamiltonians are constructed. Lastly, 4 first integrals are obtained from the analytical mechanics representations of the moving particle, and the solutions of the equations of motion are presented.[1] 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 2008 约束系统动力学研究进展 (北京: 科学出版社)]
[2] Santilli R M 1976 Foundations of Theoretical Mechanics (I) (New York: Springer-Verlag)
[3] Santilli R M 1983 Foundations of Theoretical Mechanics (II) (New York: Springer-Verlag)
[4] Lopuszanski J 1999 The Inverse Variational Problems in Classical Mechanics (Singapore: World Scientific)
[5] 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)]
[6] Nucci M C, Leach P G L 2007 J. Math. Phys. 48 123510
[7] Ding G T 2008 Acta Phys. Sin. 57 7415 (in Chinese) [丁光涛 2008 物理学报 57 7415]
[8] Ding G T 2009 Acta Phys. Sin. 58 3620 (in Chinese) [丁光涛 2009 物理学报 58 3620]
[9] Ding G T 2009 Acta Phys. Sin. 58 6725 (in Chinese) [丁光涛 2009 物理学报 58 6725]
[10] Cieslinski J L, Nikiciuk T 2010 J. Phys. A: Math. Theor. 43 17250
[11] Ding G T 2010 J. Dynam. Contr. 8 305 (in Chinese) [丁光涛 2010 动力学与控制学报 8 305]
[12] Ding G T 2011 J. Dynam. Contr. 9 102 (in Chinese) [丁光涛 2011 动力学与控制学报 9 102]
[13] Kupriyanov V G 2006 Int. J. Theor. Phys. 45 1129
[14] Gitman D M, Kupriyanov V G 2007 J. Phys. A: Math. Theor. 40 10071
[15] Ding G T 2009 Sci. China G 39 785 (in Chinese) [丁光涛 2009 中国科学G辑 39 375]
[16] 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] 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 2008 约束系统动力学研究进展 (北京: 科学出版社)]
[2] Santilli R M 1976 Foundations of Theoretical Mechanics (I) (New York: Springer-Verlag)
[3] Santilli R M 1983 Foundations of Theoretical Mechanics (II) (New York: Springer-Verlag)
[4] Lopuszanski J 1999 The Inverse Variational Problems in Classical Mechanics (Singapore: World Scientific)
[5] 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)]
[6] Nucci M C, Leach P G L 2007 J. Math. Phys. 48 123510
[7] Ding G T 2008 Acta Phys. Sin. 57 7415 (in Chinese) [丁光涛 2008 物理学报 57 7415]
[8] Ding G T 2009 Acta Phys. Sin. 58 3620 (in Chinese) [丁光涛 2009 物理学报 58 3620]
[9] Ding G T 2009 Acta Phys. Sin. 58 6725 (in Chinese) [丁光涛 2009 物理学报 58 6725]
[10] Cieslinski J L, Nikiciuk T 2010 J. Phys. A: Math. Theor. 43 17250
[11] Ding G T 2010 J. Dynam. Contr. 8 305 (in Chinese) [丁光涛 2010 动力学与控制学报 8 305]
[12] Ding G T 2011 J. Dynam. Contr. 9 102 (in Chinese) [丁光涛 2011 动力学与控制学报 9 102]
[13] Kupriyanov V G 2006 Int. J. Theor. Phys. 45 1129
[14] Gitman D M, Kupriyanov V G 2007 J. Phys. A: Math. Theor. 40 10071
[15] Ding G T 2009 Sci. China G 39 785 (in Chinese) [丁光涛 2009 中国科学G辑 39 375]
[16] 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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