Canonical transformations in three-dimensional phase space
TL;DR: Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in this paper in a general framework, and the definition of the canonical transformations is constructed as based on canonoid transformations.
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Abstract: Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them is listed. Infinitesimal canonical transformations are also discussed. Finally, we show that decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.
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Canonoid transformations and master symmetries
TL;DR: In this article, different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism, and the relation between the existence of constants of motion and the properties of canonoid symmetries is discussed.
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A Life in Mathematical Physics: Conference in Honour of Tekin Dereli
TL;DR: Tekin Dereli as discussed by the authors celebrated his 72nd birthday and the 50th year of his mathematical physics career, which was celebrated over a three-day event on 26-28 November 2021.
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Canonoid transformations and master symmetries
TL;DR: In this article, different types of transformations of a dynamical system that are compatible with the Hamiltonian structure are discussed making use of a geometric formalism, and the relation between the existence of constants of motion and the properties of canonoid symmetries is discussed.
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A treatise on the analytical dynamics of particles and rigid bodies
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The foundations of mechanics.
TL;DR: Find the secret to improve the quality of life by reading this foundations of mechanics, which can be your favorite book to read after having this book.
On foundation of the generalized Nambu mechanics
TL;DR: In this paper, a canonical formalism for the Nambu mechanics is proposed, which is based on the notion of a nambu bracket, which generalizes the Poisson bracket, a binary operation on classical observables on the phase space, to the multiple operation of higher order n ≥ 3.