Reduction and Reconstruction Aspects of Second-Order Dynamical Systems with Symmetry

被引：7

作者：

Crampin, M. ^{[1
]}

Mestdag, T. ^{[2
]}

机构：

[1] Univ Ghent, Dept Math Phys & Astron, B-9000 Ghent, Belgium

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

ACTA APPLICANDAE MATHEMATICAE | 2009年 / 105卷 / 03期

关键词：

Second-order dynamical system; Symmetry; Principal connection; Reduction; Reconstruction; EQUATIONS;

D O I：

10.1007/s10440-008-9274-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three parts and we show how the integral curves of the original system can be reconstructed from the reduced dynamics. An illustrative example confirms the results.

引用

页码：241 / 266

页数：26

共 16 条

[1]

[Anonymous], 1974, Reports on Mathematical Physics, V5, P121, DOI 10.1016/0034-4877(74)90021-4

[2]

[Anonymous], 1997, CARTANS GENERALIZATI

[3]

[Anonymous], INTERDISCIPLINARY AP

[4] Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds [J].

Bullo, Francesco ;

Lewis, Andrew D. .

ACTA APPLICANDAE MATHEMATICAE, 2007, 99 (01) :53-95

[5]

Cendra H, 2001, MEM AM MATH SOC, V152, P1

[6]

Cortes Monforte J., 2002, LECT NOTES MATH, V1793

[7] Lagrangian submanifolds and dynamics on Lie algebroids [J].

de León, M ;

Marrero, JC ;

Martínez, E .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (24) :R241-R308

[8]

Mackenzie Kirill, 1987, Lie Groupoids and Lie Algebroids in Differential Geometry, V124

[9]

Marsden J E., 1999, Texts in Applied Mathematics, Vvol 17

[10] Reduction theory and the Lagrange-Routh equations [J].

Marsden, JE ;

Ratiu, TS ;

Scheurle, J .

JOURNAL OF MATHEMATICAL PHYSICS, 2000, 41 (06) :3379-3429

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