New algorithms for constrained dynamics based on Faddeev--Jackiw approach

doi:10.1088/1009-1963/16/12/005

中国物理B ›› 2007, Vol. 16 ›› Issue (12): 3581-3588.doi: 10.1088/1009-1963/16/12/005

New algorithms for constrained dynamics based on Faddeev--Jackiw approach

许志强¹, 贾屹峰², 吴可²

(1)Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China; (2)School of Mathematical Sciences, Capital Normal University, Beijing 100037, China

出版日期:2007-12-20 发布日期:2007-12-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10401021).

New algorithms for constrained dynamics based on Faddeev--Jackiw approach

Jia Yi-Feng(贾屹峰)^a)^†, Wu Ke(吴可)^a), and Xu Zhi-Qiang(许志强)^b)

^a School of Mathematical Sciences, Capital Normal University, Beijing 100037, China; ^b Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

Online:2007-12-20 Published:2007-12-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10401021).

摘要/Abstract

摘要： In this paper, the Faddeev--Jackiw approach is improved by the Wu elimination method, so a great many complicated computations in solving constraints for the finite-dimensional polynomial-type constrained dynamics can be executed easily by using computers. Moreover, based on the Faddeev--Jackiw approach, a new algorithm of solving the constrained dynamics is presented. The new algorithm is simpler and stricter than the Faddeev--Jackiw approach. Using the new algorithm, the second Cawley counterexample is solved.

关键词: constrained, characteristic chain, symplectic matrix

Abstract: In this paper, the Faddeev--Jackiw approach is improved by the Wu elimination method, so a great many complicated computations in solving constraints for the finite-dimensional polynomial-type constrained dynamics can be executed easily by using computers. Moreover, based on the Faddeev--Jackiw approach, a new algorithm of solving the constrained dynamics is presented. The new algorithm is simpler and stricter than the Faddeev--Jackiw approach. Using the new algorithm, the second Cawley counterexample is solved.

Key words: constrained, characteristic chain, symplectic matrix

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

贾屹峰, 吴可, 许志强. New algorithms for constrained dynamics based on Faddeev--Jackiw approach[J]. 中国物理B, 2007, 16(12): 3581-3588.

Jia Yi-Feng(贾屹峰), Wu Ke(吴可), and Xu Zhi-Qiang(许志强). New algorithms for constrained dynamics based on Faddeev--Jackiw approach[J]. Chinese Physics, 2007, 16(12): 3581-3588.

[1]	刘畅, 刘世兴, 梅凤翔. Stability analysis of a simple rheonomic nonholonomic constrained system[J]. 中国物理B, 2016, 25(12): 124501-124501.
[2]	袁丽芸, 向宇, 陆静, 蒋红华. Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping[J]. 中国物理B, 2015, 24(12): 124301-124301.
[3]	高士根, 董海荣, 孙绪彬, 宁滨. Neural adaptive chaotic control with constrained input using state and output feedback[J]. , 2015, 24(1): 10501-010501.
[4]	肖夏, 徐立, 李钦伟. A double constrained robust capon beamforming based imaging method for early breast cancer detection[J]. 中国物理B, 2013, 22(9): 94101-094101.
[5]	王永龙, 卢伟涛, 蒋华, 许长谭, 潘洪哲 . Fractional charges and fractional spins for composite fermions in quantum electrodynamics[J]. 中国物理B, 2012, 21(7): 70501-070501.
[6]	王肖肖, 孙现亭, 张美玲, 韩月林, 贾利群. Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints[J]. 中国物理B, 2012, 21(5): 50201-050201.
[7]	王倩, 华宁, 唐雪正, 陆宏, 马平, 唐发宽. The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model[J]. 中国物理B, 2010, 19(8): 80601-080601.
[8]	贾利群, 解加芳, 罗绍凯. Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style[J]. 中国物理B, 2008, 17(5): 1560-1564.
[9]	王永龙, 李子平. The CP¹ nonlinear sigma model with Chern--Simons term in the Faddeev--Jachiw quantization formalism[J]. 中国物理B, 2006, 15(9): 1976-1980.
[10]	乔永芬, 赵淑红, 李仁杰. Integrating factors and conservation theorems of constrained Birkhoffian systems[J]. 中国物理B, 2006, 15(12): 2777-2781.
[11]	杨莺歌, 刘丕均, 王英, 张亚非. Extraction of optical constants and thickness of nanometre scale TiO₂ film[J]. 中国物理B, 2005, 14(11): 2335-2337.
[12]	江金环, 刘赟, 李子平. The symmetries in the Maxwell－Chern－Simons theory coupled to matter fields[J]. 中国物理B, 2004, 13(2): 153-158.
[13]	刘荣万, 陈立群. Lie symmetries and invariants of constrained Hamiltonian systems[J]. 中国物理B, 2004, 13(10): 1615-1619.
[14]	张玉峰. An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system[J]. 中国物理B, 2003, 12(11): 1194-1201.
[15]	张毅. Construction of the solution of variational equations for constrained Birkhoffian systems[J]. 中国物理B, 2002, 11(5): 437-440.

New algorithms for constrained dynamics based on Faddeev--Jackiw approach

New algorithms for constrained dynamics based on Faddeev--Jackiw approach

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0