The Maupertuis Principle and Canonical Transformations of the Extended Phase Space

DOI10.2991/JNMP.2001.8.1.12zbMATH Open0974.35118arXivnlin/0101061OpenAlexW3104949166MaRDI QIDQ2709902

A. V. Tsiganov

Publication date: 18 December 2001

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Abstract: We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals of motion, Lax equations, separated variables and action-angles variables. In this review we will discuss namely these induced transformations instead of the various parametric form of the geometric objects.

Full work available at URL: https://arxiv.org/abs/nlin/0101061

zbMATH Keywords

integrals of motioncanonical transformationsLax equationsaction-angles variables

Mathematics Subject Classification ID

Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Lattice dynamics; integrable lattice equations (37K60)

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