Abstract
This paper contains results on geometric Routh reduction and it is a continuation of a previous paper [7] where a new class of transformations is introduced between Lagrangian systems obtained after Routh reduction. In general, these reduced Lagrangian systems have magnetic force terms and are singular in the sense that the Lagrangian does not depend on some velocity components. The main purpose of this paper is to show that the Routh reduction process itself is entirely captured by the application of such a new transformation on the initial Lagrangian system with symmetry.
Highlights
A modern differential geometric treatment of Routh reduction for mechanical systems, as a Lagrangian analogue of Hamiltonian symplectic reduction, started in [14]
This paper contains results on geometric Routh reduction and it is a continuation of a previous paper [7] where a new class of transformations is introduced between Lagrangian systems obtained after Routh reduction
These reduced Lagrangian systems have magnetic force terms and are singular in the sense that the Lagrangian does not depend on some velocity components
Summary
A modern differential geometric treatment of Routh reduction for mechanical systems, as a Lagrangian analogue of Hamiltonian symplectic reduction, started in [14]. A nonAbelian version of the classical reduction procedure of Routh was developed, thereby emphasizing the role of the magnetic or gyroscopic force term which appears after reduction When taking this force term into account, the solutions of the Euler-Lagrange equations for the reduced Lagrangian, called the Routhian, are the projections of those corresponding to the original Lagrangian. We demonstrate that the process of Routh reduction may be understood as the result of two steps: the application of such a transformation to the initial Lagrangian system with symmetry, followed by a trivial reduction This indicates the importance of these transformations and sheds some new light on the geometric structure underlying Lagrangian systems with symmetry.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
