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Discrete Lagrangian Models

  • Yu.B. Suris
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 644)

Abstract

These lectures are devoted to discrete integrable Lagrangian models. A large collection of integrable models is presented in the Lagrangian fashion, along with their integrable discretizations: the Neumann system, the Garnier system, three systems from the rigid-body dynamics (multidimensional versions of the Euler top, the Lagrange top, and the top in a quadratic potential), the Clebsch case of the Kirchhoff equations for a rigid body in an ideal fluid, and certain lattice systems of the Toda type. The presentation of examples is preceded by the relevant theoretical background material on Hamiltonian mechanics on Poisson and symplectic manifolds, complete integrability and Lax representations, Lagrangian mechanics with continuous and discrete time on general manifolds and, in particular, on Lie groups.

Keywords

Poisson Bracket Lagrange Equation Lagrange Function Symplectic Manifold Poisson Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  • Yu.B. Suris
    • 1
  1. 1.Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623 BerlinGermany

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