Journal ArticleDOI
Construction of new integrable Hamiltonians in two degrees of freedom
TLDR
In this article, a new procedure for deriving integrable Hamiltonians and their constants of the motion is introduced, called the truncation program, which is a generalization of the Whittaker program.Abstract:
A new procedure for deriving integrable Hamiltonians and their constants of the motion is introduced. We term this procedure the truncation program. Integrable Hamiltonians occurring in the truncation program possess constants of the motion which are polynomials in a perturbation parameter e. The relationship between this program and the Whittaker program in two degrees of freedom is discussed. Integrable Hamiltonians occurring in the Whittaker program (a generalization of Whittaker’s work) possess constants of the motion which are polynomials in the momentum coordinates. Many previously known integrable Hamiltonians are derived. A new family of integrable double resonance Hamiltonians and a new family of integrable Hamiltonians of the form (p21+p22)/2+V(q1, q2) are derived.read more
Citations
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Direct methods for the search of the second invariant
TL;DR: In this paper, the authors discuss the direct methods that can be used to search for the second invariant of a system defined by the Hamiltonian H = 1 2 (p x 2 ) + p y 2 + A(x, y)p x + B(x and y), p y + V(x, y).
Journal ArticleDOI
Quantum groups and their applications in nuclear physics
Dennis Bonatsos,C. Daskaloyannis +1 more
TL;DR: In this article, a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis and q-oscillators), the suq(2) rotator model and its extensions, the construction of deformed exactly soluble models (u(3)so(3), model, Interacting Boson Model, Moszkowski model), the 3-dimensional q-deformed harmonic oscillator imd its relation to the nuclear shell model, and the symmetries of the anisotropic quantum harmonic oscillators with rational ratios of frequencies.
Journal ArticleDOI
Geometric integrators for ODEs
TL;DR: A survey of geometric numerical integration methods for ordinary differential equations is presented to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade.
Journal ArticleDOI
Superintegrability with third-order integrals in quantum and classical mechanics
Simon Gravel,Pavel Winternitz +1 more
TL;DR: In this paper, the coexistence of first and third-order integrals of motion in two-dimensional classical and quantum mechanics is studied, and all potentials that admit such integrals and all their integrals are found explicitly.
Journal ArticleDOI
Path Integral Discussion for Smorodinsky‐Winternitz Potentials: I. Two‐ and Three Dimensional Euclidean Space
TL;DR: In this paper, path integral formulations for the Smorodinsky-Winternitz potentials in two-and three-dimensional Euclidean space are presented, where path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave-functions are discussed.
References
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Journal ArticleDOI
Stable and Random Motions in Dynamical Systems
Jürgen Moser,Donald G. Saari +1 more
Journal ArticleDOI
Exact solution of a one-dimensional three-body scattering problem with two-body and/or three-body inverse-square potentials
Francesco Calogero,C. Marchioro +1 more
TL;DR: In this article, the exact solution of the scattering problem of three equal particles interacting in one-dimensional via two-and/or three-body inverse-square potentials is presented, and it is shown that the outcome of this scattering problem is an extremely simple relation between initial and final momenta, the latter being univocally determined by the former even in the quantal case.
Journal ArticleDOI
On the Integrability of the Toda Lattice
TL;DR: The Toda lattice has been shown to be integrably stable in a computer as discussed by the authors, where the integrability means that the system Hamiltonian can be brought to an obviously integrable form.
Book
Classical Dynamical Systems
TL;DR: In this article, the Hamiltonian Formulation of the Electrodynamic Equation of Motion has been used to describe the structure of space and time in the universe and its properties.