scholarly journals Distributed Tracking for Multiple Lagrangian Systems Using Only Position Measurements.

2014 ◽  
Vol 47 (3) ◽  
pp. 287-292 ◽  
Author(s):  
Qingkai Yang ◽  
Fengyi Zhou ◽  
Jie Chen ◽  
Xin Li ◽  
Hao Fang
Keyword(s):  
Lagrangian Systems ◽  
Distributed Tracking

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.

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