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<p>In this paper, the author first defines a regular controlled Lagrangian (RCL for short) system on a symplectic fiber bundle, establishing a good expression of the dynamical vector field of an RCL system. This dynamical vector field synthesizes the Euler-Lagrange vector field and its changes under the actions of the external force and the control. Moreover, the author describes the RCL-equivalence, the RpCL-equivalence, and the RoCL-equivalence, proving regular point and regular orbit reduction theorems for the RCL system and the regular Lagrangian system with symmetry and a momentum map. Finally, as an application the author considers the regular point reducible RCL systems on a generalization of Lie group.</p>

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Symmetric Reduction of a Regular Controlled Lagrangian System with a Momentum Map

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Hong Wang

摘要

In this paper, the author first defines a regular controlled Lagrangian (RCL for short) system on a symplectic fiber bundle, establishing a good expression of the dynamical vector field of an RCL system. This dynamical vector field synthesizes the Euler-Lagrange vector field and its changes under the actions of the external force and the control. Moreover, the author describes the RCL-equivalence, the RpCL-equivalence, and the RoCL-equivalence, proving regular point and regular orbit reduction theorems for the RCL system and the regular Lagrangian system with symmetry and a momentum map. Finally, as an application the author considers the regular point reducible RCL systems on a generalization of Lie group.