全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

Birkhoff系统的梯度表示和分数维梯度表示

Keywords: Birkhoff系统,梯度,分数维动力学

Full-Text   Cite this paper   Add to My Lib

Abstract:

研究Birkhoff系统的梯度表示和阶α=2的分数维梯度表示.首先给出Birkhoff系统成为通常梯度系统的条件.然后,给出Birkhoff系统成为阶α=2的分数维梯度系统的条件.当梯度系统的势函数V可选为Lyapunov函数时,可用Lyapunov定理来研究系统的稳定性.同时,因为梯度系统的线性化系统的特征方程仅有实根,可按Lyapunov一次近似理论来研究系统的稳定性.最后,举例说明结果的应用.

References

[1]  Tarasov V E. Fractional dynamics[M]. Beijing: Higher Education Press, 2010.
[2]  Santilli R M. Foundations of theoretical mechanicsⅡ[M]. New York: Springer-Verlag, 1983.
[3]  梅凤翔,史荣昌,张永发,等.Birkhoff系统动力学[M].北京:北京理工大学出版社,1996. Mei Fengxiang, Shi Rongchang, Zhang Yongfa, et al. Dynamics of Birkhoffian system[M]. Beijing: Beijing Institute of Technology Press, 1996. (in Chinese)
[4]  Mei F X. The Noether\'s theory of Birkhoffian systems[J]. Science in China, Series A, 1993,36(12):1456-1467.
[5]  Guo Y X, Luo S K, Shang M, et al. Birkhoffian formulations of nonholonomic constrained systems[J]. Rep on Math Phys, 2001,47(3):313-322.
[6]  张宏彬.单面约束Birkhoff系统的Noether理论[J].物理学报,2001,50(10):1837-1841. Zhang Hongbin. Noether\'s theory of Birkhoff systems with unilateral constraints [J]. Acta Phys Sin, 2001,50(10):1837-1841. (in Chinese)
[7]  Luo S K, Chen X W, Guo Y X. Theory of symmetry for a rotational relativistic Birkhoff system[J]. Chin Phys, 2002,11(5):429-436.
[8]  Zhang Y. Construction of the solution of variational equations for constrained Birkhoffian systems[J]. Chin Phys, 2002,11(5):437-440.
[9]  傅景礼,陈立群,薛纭.转动相对论Birkhoff系统的平衡稳定性[J].物理学报,2003,52(2):256-261. Fu Jingli, Chen Liquan, Xue Yun. Stability for the equilibrium state of rotational relativistic Birkhoffian systems[J]. Acta Phys Sin, 2003,52(2):256-261. (in Chinese)
[10]  Mei F X, Gang T Q, Xie J F. A symmetry and a conserved quantity for the Birkhoff system[J]. Chin Phys, 2006,15(8):1678-1681.
[11]  Shang M, Guo Y X, Mei F X. A Birkhoff-noether method of solving differential equations[J]. Chin Phys, 2007,16(2):292-295.
[12]  葛伟宽,梅凤翔.Birkhoff系统的时间积分定理[J].物理学报,2007,56(5):2479-2481. Ge Weikuan, Mei Fengxiang. Time-integral theorems for Birkhoff systems[J]. Acta Phys Sin, 2007,56(5):2479-2481. (in Chinese)

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133