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.
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Suris, Y. Discrete Lagrangian Models. In: Grammaticos, B., Tamizhmani, T., Kosmann-Schwarzbach, Y. (eds) Discrete Integrable Systems. Lecture Notes in Physics, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40357-9_5
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DOI: https://doi.org/10.1007/978-3-540-40357-9_5
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