The Maupertuis Principle and Canonical Transformations of the Extended Phase Space

2001/01/01 by Andrey Tsiganov, A.V. Tsiganov · 37 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Canonical form #Homotopy and Cohomology in Algebraic Topology #Integrable system #Lagrangian #Nonlinear Waves and Solitons #Parametric statistics #Phase (matter) #Phase space #Space (punctuation) #nlin.SI

paper · pdf · doi:10.2991/jnmp.2001.8.1.12

published in Journal of Nonlinear Mathematical Physics 8(1), 157 (Springer Nature)

arxiv created 2001/01/01 · openalex publication_date 2001/01/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Duality between integrable Stäckel systems
• THE STRUCTURES OF HAMILTONIAN MECHANICS
• Regularization of kepler's problem and the averaging method on a manifold
• Integrable quartic potentials and coupled KdV equations
• The Lax pairs for the Holt system