scholarly journals Routh reduction and the class of magnetic Lagrangian systems

2012 ◽  
Vol 53 (6) ◽  
pp. 062902 ◽  
Author(s):  
B. Langerock ◽  
E. García-Toraño Andrés ◽  
F. Cantrijn
Keyword(s):  
Lagrangian Systems ◽  
Routh Reduction

scholarly journals ROUTH REDUCTION FOR SINGULAR LAGRANGIANS

2010 ◽  
Vol 07 (08) ◽  
pp. 1451-1489 ◽  
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.

scholarly journals A note on Hybrid Routh reduction for time-dependent Lagrangian systems

2020 ◽  
Vol 12 (2) ◽  
pp. 309-321
Author(s):  
Leonardo J. Colombo ◽  
◽  
María Emma Eyrea Irazú ◽  
Eduardo García-Toraño Andrés ◽  
◽  
...  
Keyword(s):  
Time Dependent ◽  
Lagrangian Systems ◽  
Routh Reduction

Onset of instability for a class of nonlinear lagrangian systems

1982 ◽  
Vol 91 (8) ◽  
pp. 378-380 ◽  
Author(s):  
E.W. Laedke ◽  
K.H. Spatschek ◽  
M. Wilkens
Keyword(s):  
Lagrangian Systems ◽  
Nonlinear Lagrangian

Global minimizers for Tonelli Lagrangians on the 2-torus

2015 ◽  
Vol 07 (02) ◽  
pp. 261-291 ◽  
Author(s):  
Jan Philipp Schröder
Keyword(s):  
Energy Levels ◽  
Critical Value ◽  
Lagrangian Systems ◽  
Global Minimizers ◽  
Fixed Energy

We study action-minimizing orbits in Tonelli Lagrangian systems on the 2-torus on fixed energy levels above Mañé's strict critical value. Our work generalizes the results of Morse, Hedlund and Bangert on minimal geodesics in Riemannian 2-tori. The techniques in the proofs involve classical variational ones, as well as the theories of Mather, Mañé and Fathi, which allow the step from reversible to non-reversible dynamics.

Resilient Leader Tracking for Networked Lagrangian Systems Under DoS Attacks

2021 ◽  
Author(s):  
Xiaolei Li ◽  
Changyun Wen ◽  
Jiange Wang ◽  
Ci Chen ◽  
Chao Deng
Keyword(s):  
Lagrangian Systems ◽  
Dos Attacks ◽  
Networked Lagrangian Systems
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