Routh Reduction by Stages

Routh reduction for first-order Lagrangian field theories

Letters in Mathematical Physics ◽

10.1007/s11005-018-1140-6 ◽

2018 ◽

Vol 109 (6) ◽

pp. 1343-1376

Author(s):

Santiago Capriotti ◽

Eduardo García-Toraño Andrés

Keyword(s):

Field Theories ◽

First Order ◽

Routh Reduction

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Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2018-0037 ◽

2019 ◽

Vol 20 (3-4) ◽

pp. 293-302

Author(s):

Ivan Polekhin

Keyword(s):

Fixed Point ◽

Rigid Body ◽

Integrable Case ◽

Analytical Results ◽

Routh Reduction ◽

Gyroscopic Forces ◽

Kovalevskaya Case

AbstractThe problem of motion of a rigid body with a fixed point is considered. We study qualitatively the solutions of the system after Routh reduction. For the Lagrange integrable case, we show that the trajectories of solutions starting at the boundary of a possible motion area can both cover and not cover the entire possible motion area. It distinguishes these systems from the systems without gyroscopic forces, where the trajectories always cover the possible motion area. We also present some numerical and analytical results on the same matter for the Kovalevskaya case.

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Dynamic Analysis of Tippe Top on Cylinder’s Inner Surface With and Without Friction based on Routh Reduction

Journal of Physics Conference Series ◽

10.1088/1742-6596/1467/1/012040 ◽

2020 ◽

Vol 1467 ◽

pp. 012040

Author(s):

M Ariska ◽

H Akhsan ◽

M Muslim

Keyword(s):

Dynamic Analysis ◽

Inner Surface ◽

Tippe Top ◽

Routh Reduction

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ROUTH REDUCTION FOR SINGULAR LAGRANGIANS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887810004907 ◽

2010 ◽

Vol 07 (08) ◽

pp. 1451-1489 ◽

Cited By ~ 5

Author(s):

BAVO LANGEROCK ◽

MARCO CASTRILLÓN LÓPEZ

Keyword(s):

Kinetic Energy ◽

Original System ◽

Regularity Conditions ◽

Lagrangian Systems ◽

Lagrange Equations ◽

Reduction Procedure ◽

Momentum Map ◽

Routh Reduction ◽

Regular Value ◽

Singular Lagrangians

This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian L or the momentum map JL are required apart from the momentum being a regular value of JL. The main results of this paper are: the description of a general Routh reduction procedure that preserves the Euler–Lagrange nature of the original system and the presentation of a presymplectic framework for Routh reduced systems. In addition, we provide a detailed description and interpretation of the Euler–Lagrange equations for the reduced system. The proposed procedure includes Lagrangian systems with a non-positively definite kinetic energy metric.

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