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针对非完整系统的Boltzmann-Hamel方程, 当其满足一定条件时, 可以进行广义Birkhoff化.构造生成函数, 利用当前比较优越的非自治Birkhoff广义辛算法对其进行数值仿真. 仿真结果和传统的Runge-Kutta算法结果相比较, 非自治Birkhoff广义辛算法在长期跟踪后更加准确.
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关键词:
- 非完整约束 /
- Boltzmann-Hamel方程 /
- Birkhoff辛算法
For a Boltzmann-Hamel equation of nonholonomic mechanical system, when it meets certain conditions, the Boltzmann-Hamel equation can be transformed into a Birkhoffian system. By constructing the generating function, the system is investigated numerically using the generalized symplectic geometric algorithm of the nonautonomous Birkhoffian system. Compared with the above-mentioned algorithm with the classical Runge-Kutta method, Birkhoffian symplectic scheme is very accurate in a long-term tracing.[1] Boltzmann L 1902 Sitz. Math. Natur. Akad. Wiss. B 11 1603
[2] Hame1 G 1904 Math. Phys. 50 1
[3] Hamel G 1938 Art. Sitz. Math. Ges. 37 4
[4] Mei F X 1983 Transactions of Beijing Institute of Technology 2 22 (in Chinese) [梅凤翔 1983 北京工业学院学报 2 22]
[5] Mei F X 1985 The Foundations of Mechanics of Nonholonomic System (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整系统力学基础 (北京:北京工业学院出版社)]
[6] Zhang J F 1990 Huanghuai Journal 6 13 (in Chinese) [张解放 1990 黄淮学刊 6 13]
[7] Luo S K 1990 Huanghuai Journal 6 23 (in Chinese) [罗绍凯 1990 黄淮学刊 6 23]
[8] Luo S K 1992 Chinese Science Bulletin 37 93 (in Chinese) [罗绍凯 1992 科学通报 37 93]
[9] Chen L Q 1994 Huanghuai Journal 10 8 (in Chinese) [陈立群 1994 黄淮学刊 10 8]
[10] Lü Z Q 1994 Jiangxi Science 12 195 (in Chinese) [吕哲勤 1994 江西科学 12 195]
[11] Feng K 1985 Proc of the 1984 Beijing Symposium on Differential Geometry and Differential Equationgs Computation of Partial Differential Equations (Beijing: Science Press)
[12] Guo Y X, Song Y B, Zhang X B, Chi D P 2003 Chin. Phys. Lett. 20 1192
[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] Luo S K 1990 Journal of Yiyang Teachers College 1 32 (in Chinese) [罗绍凯 1990 益阳师专学报 1 32]
[16] Zhang J F, Zhang H Z 1990 Journal of Zhejiang Normal University 13 61 (in Chinese) [张解放, 张洪忠 1990 浙江师范大学学报 13 61]
[17] Su H L 2004 Commun. Theor. Phys. 53 476
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[1] Boltzmann L 1902 Sitz. Math. Natur. Akad. Wiss. B 11 1603
[2] Hame1 G 1904 Math. Phys. 50 1
[3] Hamel G 1938 Art. Sitz. Math. Ges. 37 4
[4] Mei F X 1983 Transactions of Beijing Institute of Technology 2 22 (in Chinese) [梅凤翔 1983 北京工业学院学报 2 22]
[5] Mei F X 1985 The Foundations of Mechanics of Nonholonomic System (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整系统力学基础 (北京:北京工业学院出版社)]
[6] Zhang J F 1990 Huanghuai Journal 6 13 (in Chinese) [张解放 1990 黄淮学刊 6 13]
[7] Luo S K 1990 Huanghuai Journal 6 23 (in Chinese) [罗绍凯 1990 黄淮学刊 6 23]
[8] Luo S K 1992 Chinese Science Bulletin 37 93 (in Chinese) [罗绍凯 1992 科学通报 37 93]
[9] Chen L Q 1994 Huanghuai Journal 10 8 (in Chinese) [陈立群 1994 黄淮学刊 10 8]
[10] Lü Z Q 1994 Jiangxi Science 12 195 (in Chinese) [吕哲勤 1994 江西科学 12 195]
[11] Feng K 1985 Proc of the 1984 Beijing Symposium on Differential Geometry and Differential Equationgs Computation of Partial Differential Equations (Beijing: Science Press)
[12] Guo Y X, Song Y B, Zhang X B, Chi D P 2003 Chin. Phys. Lett. 20 1192
[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] Luo S K 1990 Journal of Yiyang Teachers College 1 32 (in Chinese) [罗绍凯 1990 益阳师专学报 1 32]
[16] Zhang J F, Zhang H Z 1990 Journal of Zhejiang Normal University 13 61 (in Chinese) [张解放, 张洪忠 1990 浙江师范大学学报 13 61]
[17] Su H L 2004 Commun. Theor. Phys. 53 476
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