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采用辛几何算法对广义力具有广义势的特殊Chaplygin系统的动力学性质进行数值研究,并和传统的Runge-Kutta算法进行比较,得出辛几何算法在这类非完整力学系统的计算中具有优越性.
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关键词:
- 辛几何算法 /
- Chaplygin系统 /
- Helmholtz条件
A special Chaplygin system is studied numerically by using the symplectic geometric algorithm and compared with the classical R-K method. By comparing the results of the two methods, the advantage of symplectic geometric algorithm used on this special Chaplygin mechanical system is demonstrated.[1] Cort'es J, Geometric, 2002 Control and Numerical Aspects of Nonholonomic Systems (Berlin: Springer)
[2] Mei F X, Liu D, Luo Y 1991 Advanced Analytical Mechanics(Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔、刘 瑞、罗 勇 1991 高等分析力学(北京:北京理工大学出版社)]
[3] Ostrowsky J 1998 Rep. Math. Phys. 42 185
[4] Wang Y, Guo Y X, Lü Q S, Liu C 2009 Acta Phys. Sin. 58 5142 (in Chinese) [王 勇、郭永新、吕群松、刘 畅2009 58 5142]
[5] Liu C, Chang P, Liu S X, Guo Y X 2010 Chin. Phys. B 19 030302
[6] Pang T, Fang J H, Zhang M J, Lin P, Lu K 2009 Chin. Phys. B 18 3150
[7] Ge W K, 2009 Acta Phys. Sin. 58 6729(in Chinese)[葛伟宽 2009 58 6729]
[8] Liu S X, Guo Y X, Liu C 2008 Acta Phys. Sin. 57 1311(in Chinese)[刘世兴、郭永新、刘 畅 2008 57 1311]
[9] Feng K 1985 Proc. of the 1984 Beijing Symposium on Differential Geometry and Differential Equations Computation of Partial Differential Equations, edited by Feng K (Beijing: Science Press) P42—58
[10] Liu X S, Ding P Z 2004 Adv. Phys. 26 48 (in Chinese)[刘学深、丁培柱 2004 物理学进展26 48]
[11] Guo Y X, Song Y B, Zhang X B, Chi D P 2003 Chin. Phys. Lett. 20 1192
[12] Wang Y, Guo Y X 2005 Acta Phys. Sin. 54 5517 (in Chinese)[王 勇、郭永新2005 54 5517]
[13] Guo Y X, Shang M, Luo S K, Mei F X 2001 Int. J. Theor Phys. 40 1197
[14] Guo Y X, Luo S K, Shang M, Mei F X 2001 Rep. Math. Phys. 47 313
[15] Guo Y X, Mei F X 1999 Int. J. Theor Phys. 38 1017
[16] Zhu W S, Zhao X S, Tang YQ 1996 J. Chem. Phys. 104 2275
[17] Yoshida H 1990 Phys. Lett.A 150 262
[18] Santilli R M 1978 Foundations of Theoretical Mechanics I (New York: Springer-verlag.)
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[1] Cort'es J, Geometric, 2002 Control and Numerical Aspects of Nonholonomic Systems (Berlin: Springer)
[2] Mei F X, Liu D, Luo Y 1991 Advanced Analytical Mechanics(Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔、刘 瑞、罗 勇 1991 高等分析力学(北京:北京理工大学出版社)]
[3] Ostrowsky J 1998 Rep. Math. Phys. 42 185
[4] Wang Y, Guo Y X, Lü Q S, Liu C 2009 Acta Phys. Sin. 58 5142 (in Chinese) [王 勇、郭永新、吕群松、刘 畅2009 58 5142]
[5] Liu C, Chang P, Liu S X, Guo Y X 2010 Chin. Phys. B 19 030302
[6] Pang T, Fang J H, Zhang M J, Lin P, Lu K 2009 Chin. Phys. B 18 3150
[7] Ge W K, 2009 Acta Phys. Sin. 58 6729(in Chinese)[葛伟宽 2009 58 6729]
[8] Liu S X, Guo Y X, Liu C 2008 Acta Phys. Sin. 57 1311(in Chinese)[刘世兴、郭永新、刘 畅 2008 57 1311]
[9] Feng K 1985 Proc. of the 1984 Beijing Symposium on Differential Geometry and Differential Equations Computation of Partial Differential Equations, edited by Feng K (Beijing: Science Press) P42—58
[10] Liu X S, Ding P Z 2004 Adv. Phys. 26 48 (in Chinese)[刘学深、丁培柱 2004 物理学进展26 48]
[11] Guo Y X, Song Y B, Zhang X B, Chi D P 2003 Chin. Phys. Lett. 20 1192
[12] Wang Y, Guo Y X 2005 Acta Phys. Sin. 54 5517 (in Chinese)[王 勇、郭永新2005 54 5517]
[13] Guo Y X, Shang M, Luo S K, Mei F X 2001 Int. J. Theor Phys. 40 1197
[14] Guo Y X, Luo S K, Shang M, Mei F X 2001 Rep. Math. Phys. 47 313
[15] Guo Y X, Mei F X 1999 Int. J. Theor Phys. 38 1017
[16] Zhu W S, Zhao X S, Tang YQ 1996 J. Chem. Phys. 104 2275
[17] Yoshida H 1990 Phys. Lett.A 150 262
[18] Santilli R M 1978 Foundations of Theoretical Mechanics I (New York: Springer-verlag.)
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