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The Maupertuis principle and canonical transformations of the extended phase space

Andrey Tsiganov
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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.

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Andrey Tsiganov. 2001-01-01. The Maupertuis principle and canonical transformations of the extended phase space. https://doi.org/10.2991/jnmp.2001.8.1.12

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