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First integrals for some nonlinear time‐dependent Hamiltonian systems
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In this article, an observation of a simple property of canonical transformations leads to a procedure for determining first integrals for classes of Hamiltonians, and the most general result presently known from other methods is recovered, a new result presented, and a generalization to more than one degree of freedom discussed.Abstract:
An observation of a simple property of canonical transformations leads to a procedure for determining first integrals for classes of Hamiltonians. In illustrative examples the most general result presently known from other methods is recovered, a new result presented, and a generalization to more than one degree of freedom discussed.read more
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First integrals versus configurational invariants and a weak form of complete integrability
TL;DR: In this paper, a confusion over the concept of first integrals was clarified, and the clear distinction between first-integrals and functions which are first-independents only on a specific, fixed hypersurface was discussed.
Journal ArticleDOI
Dynamical symmetries and the Ermakov invariant
Fernando Haas,J. Goedert +1 more
TL;DR: Ermakov systems possessing Noether point symmetry were identified in this paper, and the Ermakov invariant was shown to result from an associated symmetry of dynamical character, which is sufficient to reduce these systems to quadratures.
Journal ArticleDOI
First integrals and symmetries of time‐dependent Hamiltonian systems
Alain Dewisme,Serge Bouquet +1 more
TL;DR: In this paper, the authors studied the first integrals of one-dimensional time-dependent Hamiltonians, H(q,p,t), and derived a technique leading to a first integral from a Lie symmetry, which was used to completely integrate a special case of the linear harmonic oscillator with a timedependent frequency.
Journal ArticleDOI
Representations of one‐dimensional Hamiltonians in terms of their invariants
TL;DR: In this paper, a general formalism for representing the Hamiltonian of a system with one degree of freedom in terms of its invariants is developed, for which any particular function I(q,p,t) is an invariant.
Journal ArticleDOI
Berry's phase and wavefunctions for time-dependent Hamilton systems
TL;DR: An alternative derivation of Berry's phase (1985) to that given by Morales (1988) is given for non-autonomous Hamiltonian systems which admit an energy-like first integral as discussed by the authors.
References
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Journal ArticleDOI
Invariants and wavefunctions for some time‐dependent harmonic oscillator‐type Hamiltonians
TL;DR: In this article, it was shown that an oscillator with source undergoing translation, the two-dimensional anisotropic oscillator, general one-dimensional oscillators with Hamiltonians of homogeneous quadratic form, can be transformed to the time-independent Hamiltonian, H= (1/2) ωTω, by a time-dependent linear canonical transformation, ω=Sω+r.
Journal ArticleDOI
An exact invariant for a class of time‐dependent anharmonic oscillators with cubic anharmonicity
TL;DR: In this paper, an exact invariant for a class of time-dependent anharmonic oscillators using the method of the Lie theory of extended groups was constructed for a subclass of oscillators.
Journal ArticleDOI
Exact invariants for a class of time-dependent nonlinear Hamiltonian systems
H. Ralph Lewis,P. G. L. Leach +1 more
TL;DR: In this paper, a method of generalizing a class of invariants for a time-dependent linear oscillator is developed for the motion of a mass point in one dimension with a general timedependent nonlinear potential.
Journal ArticleDOI
A direct construction of first integrals for certain non-linear dynamical systems
Willy Sarlet,Leon Y. Bahar +1 more
TL;DR: In this article, a constructive approach to the problem of finding first integrals of certain non-linear, second order ordinary differential equations is presented, motivated by the construction of the energy integral for the equations of motion of the corresponding conservative systems.
Journal ArticleDOI
Adiabatic invariants for dynamical systems with one degree of freedom
TL;DR: Adiabatic invariants for dynamical systems with one degree of freedom, whose equation of motion is (1), and where the existence of the corresponding Hamilton action integral is not imposed, are established in this article.
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