Skew-gradient representations of constrained mechanical systems

doi:10.1007/s10483-015-1954-9

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (7): 873-882.doi: https://doi.org/10.1007/s10483-015-1954-9

Skew-gradient representations of constrained mechanical systems

Fengxiang MEI¹, Jinchao CUI²

1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;
2. School of Science, Jiangnan University, Wuxi 214122, Jiangsu Province, China

收稿日期:2014-11-20 修回日期:2014-12-24 出版日期:2015-07-01 发布日期:2015-07-01
通讯作者: Jinchao CUI E-mail:cjcwx@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 10932002 and 11272050)

Skew-gradient representations of constrained mechanical systems

Fengxiang MEI¹, Jinchao CUI²

1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;
2. School of Science, Jiangnan University, Wuxi 214122, Jiangsu Province, China

Received:2014-11-20 Revised:2014-12-24 Online:2015-07-01 Published:2015-07-01
Contact: Jinchao CUI E-mail:cjcwx@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 10932002 and 11272050)

摘要/Abstract

摘要： The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Hamiltonian systems are given. The characteristics of skew-gradient systems are used to study integration and stability of the solution of constrained mechanical systems. Examples are given to illustrate applications of the result.

关键词: stability, skew-gradient system, constrained mechanical system, integration

Abstract: The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Hamiltonian systems are given. The characteristics of skew-gradient systems are used to study integration and stability of the solution of constrained mechanical systems. Examples are given to illustrate applications of the result.

Key words: skew-gradient system, constrained mechanical system, integration, stability

中图分类号:

O316

Fengxiang MEI, Jinchao CUI. Skew-gradient representations of constrained mechanical systems[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(7): 873-882.

参考文献

[1] Hirsch, M. W. and Smale, S. Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York (1974)
[2] McLachlan, R. I., Quispel, G. R. W., and Robidoux, N. Geometric integration using discrete gradients. Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 357(1754), 1021-1045 (1999)
[3] Hirsch, M. W. and Smale, S. Discrete Gradient Methods for Solving ODEs Numerically while Preserving a First Integral, La Trobe University Press, Melbourne (1996)
[4] Yanagida, E. Mini-maximizers for reaction-diffusion systems with skew-gradient structure. Journal of Differential Equations, 179(1), 311-335 (2002)
[5] Pego, R. L. Stabilization in a gradient system with a conservation law. Proceedings of the American Mathematical Society, 114(4), 1017-1024 (1992)
[6] Mei, F. X. On the gradient system (in Chinese). Mechanics in Engineering, 34(1), 89-90 (2012)
[7] Mei, F. X. On the skew-gradient system (in Chinese). Mechanics in Engineering, 35(5), 79-81 (2013)
[8] Mei, F. X. and Wu, H. B. A gradient representation for generalized Birkhoff system (in Chinese). Journal of Dynamics and Control, 10(4), 289-292 (2012)
[9] Mei, F. X. andWu, H. B. Generalized Hamilton system and gradient system (in Chinese). Scientia Sinica: Physica, Mechanica and Astronomica, 43(4), 538-540 (2013)
[10] Mei, F. X., Cui, J. C., and Wu, H. B. A gradient representation and a fractional gradient repre- sentation of Birkhoff system (in Chinese). Transactions of Beijing Institute of Technology, 32(12), 1298-1300 (2012)
[11] Mei, F. X. Analytical Mechanics II (in Chinese). Beijing Institute of Technology Press, Beijing (2013)
[12] Santilli, R. M. Foundations of Theoretical Mechanics II, Springer-Verlag, New York (1983)
[13] Mei, F. X., Shi, R. C., Zhang, Y. F., and Wu, H. B. Dynamics of Birkhoffian System (in Chinese), Beijing Institute of Technology Press, Beijing (1996)
[14] Mei, F. X. Dynamics of Generalized Birkhoffian System (in Chinese), Science Press, Beijing (2013)
[15] Li, J. B., Zhao, X. H., and Liu, Z. R. Theory and Its Application of Generalized Hamilton System (in Chinese), Science Press, Beijing (1994)

Skew-gradient representations of constrained mechanical systems

Skew-gradient representations of constrained mechanical systems

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