scholarly journals Geodesics in stationary spacetimes and classical Lagrangian systems

2007 ◽  
Vol 232 (1) ◽  
pp. 253-276 ◽  
Author(s):  
Anna Germinario
Keyword(s):  
Lagrangian Systems ◽  
Stationary Spacetimes ◽  
Classical Lagrangian

scholarly journals Fermat Metrics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1422
Author(s):  
Antonio Masiello
Keyword(s):  
Variational Methods ◽  
Morse Theory ◽  
Sagnac Effect ◽  
Variational Theory ◽  
Global Hyperbolicity ◽  
Fermat Principle ◽  
Multiple Image ◽  
Light Rays ◽  
Stationary Spacetimes

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

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.

scholarly journals Separable geodesic action slicing in stationary spacetimes

2011 ◽  
Vol 44 (3) ◽  
pp. 603-621 ◽  
Author(s):  
Donato Bini ◽  
Andrea Geralico ◽  
Robert T. Jantzen
Keyword(s):  
Stationary Spacetimes

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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