Journal ArticleDOI
A theory of exact and approximate configurational invariants
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TLDR
In this paper, a theory of integrable Hamiltonian systems in two dimensions is presented, which admits to integrability of the orbits for magnetic or Coriolis forces as well as for forces derivable from a potential.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1983-07-01. It has received 96 citations till now. The article focuses on the topics: Invariant (mathematics) & Superintegrable Hamiltonian system.read more
Citations
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Book ChapterDOI
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS
Journal ArticleDOI
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
The He´non-Heiles system revisited
TL;DR: In this paper, the known integrable cases of the Henon-Heiles system are shown to be closely related to the stationary flows of the known (and only) integrably fifth-order (single component and polynomial) nonlinear evolution equations.
Journal ArticleDOI
Painlevé analysis, Lie symmetries, and integrability of coupled nonlinear oscillators of polynomial type
M. Lakshmanan,R. Sahadevan +1 more
TL;DR: In this paper, the authors apply the singularity structure analysis to the analysis of nonlinear dynamical systems, starting from simple examples of coupled nonlinear oscillators governed by generic Hamiltonians of polynomial type with two, three and arbitrary degrees of freedom.
Journal ArticleDOI
Integrable Hamiltonian Systems With Velocity Dependent Potentials
TL;DR: In this paper, the integrability of a two-dimensional Hamiltonian in which the potential depends explicitly on the momenta is investigated, and two integrable classes of potentials are identified and the second integral of motion is constructed for each of them.
References
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Book
Perturbation Methods
Ali H. Nayfeh,Vimal Singh +1 more
TL;DR: This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.
Journal ArticleDOI
A universal instability of many-dimensional oscillator systems
TL;DR: In this article, the authors demonstrate the mechanism for a universal instability, the Arnold diffusion, which occurs in the oscillating systems having more than two degrees of freedom, which results in an irregular, or stochastic, motion of the system as if the latter were influenced by a random perturbation even though, in fact, the motion is governed by purely dynamical equations.
Book
A treatise on the analytical dynamics of particles and rigid bodies
TL;DR: In this article, a comprehensive account of analytical dynamics is given, starting from first principles with kinematics before moving to equations of motion and specific and explicit methods for solving them, with chapters devoted to particle dyanmics, rigid bodies, vibration and dissipative systems.
Journal ArticleDOI
The applicability of the third integral of motion: Some numerical experiments
Michel Henon,Carl Heiles +1 more
TL;DR: In this paper, the existence of a third isolating integral of motion in an axisymmetric potential was investigated by numerical experiments and it was found that the third integral exists for only a limited rage of initial conditions.