A connection theory for a nonlinear differential constrained system

doi:10.1088/1009-1963/11/12/302

中国物理B ›› 2002, Vol. 11 ›› Issue (12): 1228-1233.doi: 10.1088/1009-1963/11/12/302

A connection theory for a nonlinear differential constrained system

许志新¹, 郭永新², 吴炜²

(1)Department No. 1, East China Shipbuilding Institute, Zhenjiang 212003, China; (2)Department of Physics, Liaoning University, Shenyang 110036, China

收稿日期:2002-05-14 修回日期:2002-08-16 出版日期:2002-12-12 发布日期:2005-06-12
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10175032), the Natural Science Foundation of Liaoning Province, China (Grant Nos 002083 and 2001101024), and the Science Research Foundation of Liaoning Education Bureau, China (Grant Nos 990111004 and 20021004).

A connection theory for a nonlinear differential constrained system

Xu Zhi-Xin (许志新)^a, Guo Yong-Xin (郭永新)^b, Wu Wei (吴炜)^b

^a Department No. 1, East China Shipbuilding Institute, Zhenjiang 212003, China; ^b Department of Physics, Liaoning University, Shenyang 110036, China

Received:2002-05-14 Revised:2002-08-16 Online:2002-12-12 Published:2005-06-12
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10175032), the Natural Science Foundation of Liaoning Province, China (Grant Nos 002083 and 2001101024), and the Science Research Foundation of Liaoning Education Bureau, China (Grant Nos 990111004 and 20021004).

摘要/Abstract

摘要： An Ehresmann connection on a constrained state bundle defined by nonlinear differential constraints is constructed for nonlinear nonholonomic systems. A set of differential constraints is integrable if and only if the curvature of the Ehresmann connection vanishes. Based on a geometric interpretation of d－δ commutation relations in constrained dynamics given in this paper, the complete integrability conditions for the differential constraints are proven to be equivalent to the three requirements upon the conditional variation in mechanics: (1) the variations belong to the constrained manifold; (2) the time derivative commutes with variational operator; (3) the variations satisfy the Chetaev's conditions.

Abstract: An Ehresmann connection on a constrained state bundle defined by nonlinear differential constraints is constructed for nonlinear nonholonomic systems. A set of differential constraints is integrable if and only if the curvature of the Ehresmann connection vanishes. Based on a geometric interpretation of $d-\delta$ commutation relations in constrained dynamics given in this paper, the complete integrability conditions for the differential constraints are proven to be equivalent to the three requirements upon the conditional variation in mechanics: (1) the variations belong to the constrained manifold; (2) the time derivative commutes with variational operator; (3) the variations satisfy the Chetaev's conditions.

Key words: constraint, Ehresmann connection, integrability condition, $d-\delta$ commutation relation

中图分类号: (Ordinary differential equations)

02.30.Hq

02.40.-k (Geometry, differential geometry, and topology) 02.30.Cj (Measure and integration)

许志新, 郭永新, 吴炜. A connection theory for a nonlinear differential constrained system[J]. 中国物理B, 2002, 11(12): 1228-1233.

Xu Zhi-Xin (许志新), Guo Yong-Xin (郭永新), Wu Wei (吴炜). A connection theory for a nonlinear differential constrained system[J]. Chinese Physics, 2002, 11(12): 1228-1233.

[1]	Bin He(何斌) and Qing Meng(蒙清). Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation[J]. 中国物理B, 2021, 30(6): 60201-060201.
[2]	师利娟, 温振庶. Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation[J]. 中国物理B, 2019, 28(4): 40201-040201.
[3]	温振庶, 师利娟. Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation[J]. 中国物理B, 2018, 27(9): 90201-090201.
[4]	王金环, 许玉玲, 张建, 杨德东. Time-varying formation for general linear multi-agent systems via distributed event-triggered control under switching topologies[J]. 中国物理B, 2018, 27(4): 40504-040504.
[5]	金世欣, 张毅. Generalized Chaplygin equations for nonholonomic systems on time scales[J]. 中国物理B, 2018, 27(2): 20502-020502.
[6]	韩青爽, 陈帝伊, 张浩. Bursting oscillations in a hydro-turbine governing system with two time scales[J]. 中国物理B, 2017, 26(12): 128202-128202.
[7]	鲍江宏, 陈丹丹. Coexisting hidden attractors in a 4D segmented disc dynamo with one stable equilibrium or a line equilibrium[J]. 中国物理B, 2017, 26(8): 80201-080201.
[8]	张翔, 王金环, 杨德东, 徐勇. Tracking consensus for nonlinear heterogeneous multi-agent systems subject to unknown disturbances via sliding mode control[J]. 中国物理B, 2017, 26(7): 70501-070501.
[9]	R Saravanakumar, M Syed Ali. Robust H_∞ control for uncertain Markovian jump systems with mixed delays[J]. 中国物理B, 2016, 25(7): 70201-070201.
[10]	Hakan Ciftci, H F Kisoglu. Application of asymptotic iteration method to a deformed well problem[J]. 中国物理B, 2016, 25(3): 30201-030201.
[11]	F M Abbasi, M Mustafa, S A Shehzad, M S Alhuthali, T Hayat. Analytical study of Cattaneo-Christov heat flux model for a boundary layer flow of Oldroyd-B fluid[J]. 中国物理B, 2016, 25(1): 14701-014701.
[12]	刘期怀, 邢明燕, 李新祥, 王超. Unstable and exact periodic solutions of three-particles time-dependent FPU chains[J]. 中国物理B, 2015, 24(12): 120401-120401.
[13]	M. Syed Ali, R. Saravanakumar. Robust H_∞ control of uncertain systems with two additive time-varying delays[J]. 中国物理B, 2015, 24(9): 90202-090202.
[14]	M. Syed Ali, R. Saravanakumar. Augmented Lyapunov approach to H_∞ state estimation of static neural networks with discrete and distributed time-varying delays[J]. 中国物理B, 2015, 24(5): 50201-050201.
[15]	M. Syed Ali, R. Saravanakumar. Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays[J]. , 2014, 23(12): 120201-120201.

A connection theory for a nonlinear differential constrained system

A connection theory for a nonlinear differential constrained system

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