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| Symmetric Reduction of a Regular Controlled Lagrangian System with a Momentum Map |
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Citation： |
Hong WANG.Symmetric Reduction of a Regular Controlled Lagrangian System with a Momentum Map[J].Chinese Annals of Mathematics B,2026,(1):71~100 |
| Page view： 183
Net amount： 94 |
Authors： |
Hong WANG; |
Foundation： |
the National Natural Science Foundation of China (No. 11531011), the
Nankai University 985 Project and the Key Laboratory of Pure Mathematics and Combinatorics, Ministry of Education, China. |
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| Abstract： |
In this paper, the author first defines a regular controlled Lagrangian (R-CL) system on a symplectic fiber bundle and introduces the notion of RCL-equivalence. Then, using momentum maps, two types of symmetric reduction—regular point reduction and regular orbit reduction—are established for R-CL systems. The reduced systems are shown to retain the R-CL structure, and the equivalence between the original and reduced systems is verified under suitable conditions. |
Keywords： |
Regular controlled Lagrangian system Legendre transformation RCL-equivalence Momentum map Regular point reduction Regular orbit reduction |
Classification： |
70H33, 53D20, 70Q05 |
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