An independence theorem for Lagrangian systems on graded manifolds

1984 ◽  
Vol 8 (2) ◽  
pp. 105-109 ◽  
Author(s):  
Andrea Barducci ◽  
Riccardo Giachetti ◽  
Emanuele Sorace
Keyword(s):  
Lagrangian Systems ◽  
Independence Theorem ◽  
Graded Manifolds

GRADED LAGRANGIAN FORMALISM

2013 ◽  
Vol 10 (05) ◽  
pp. 1350016 ◽  
Author(s):  
G. SARDANASHVILY
Keyword(s):  
Classical Field Theory ◽  
General Setting ◽  
Classical Field ◽  
Lagrangian Formalism ◽  
Lagrangian Systems ◽  
Comprehensive Description ◽  
Variational Bicomplex ◽  
Gauge Symmetries ◽  
Degenerate Lagrangian ◽  
Graded Manifolds

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems, characterized by hierarchies of non-trivial higher-order Noether identities and gauge symmetries. This is a general case of classical field theory and Lagrangian non-relativistic mechanics.

scholarly journals Quantized fault‐tolerant consensus for multiple Lagrangian systems subject to switching networks

2021 ◽  
Author(s):  
Xiang‐Yu Yao ◽  
Ju H. Park ◽  
Hua‐Feng Ding ◽  
Ming‐Feng Ge
Keyword(s):  
Fault Tolerant ◽  
Lagrangian Systems ◽  
Switching Networks

scholarly journals Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds

2020 ◽  
Vol 8 (1) ◽  
pp. 68-91
Author(s):  
Gianmarco Giovannardi
Keyword(s):  
Characteristic Direction ◽  
Fixed Degree ◽  
One Dimensional ◽  
First Order ◽  
Natural Choice ◽  
Higher Dimensional ◽  
Graded Manifold ◽  
The One ◽  
Graded Manifolds ◽  
Holonomy Map

AbstractThe deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

scholarly journals THE EXTENDED Λ-METHOD FOR CONTROLLED LAGRANGIAN SYSTEMS

2005 ◽  
Vol 38 (1) ◽  
pp. 592-597 ◽  
Author(s):  
Dong Eui Chang
Keyword(s):  
Lagrangian Systems

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

Asymptotic solutions of Lagrangian systems with gyroscopic forces

1995 ◽  
Vol 2 (4) ◽  
pp. 417-444 ◽  
Author(s):  
Sergey Bolotin ◽  
Piero Negrini
Keyword(s):  
Asymptotic Solutions ◽  
Lagrangian Systems ◽  
Gyroscopic Forces
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