The Lissajous transformation. II: Normalization

DOI10.1007/BF00051692zbMath0756.70015OpenAlexW2092816024MaRDI QIDQ1186235

André Deprit, Antonio Elipe

Publication date: 28 June 1992

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00051692

zbMATH Keywords

cylindrical coordinatesreductionHamiltonian systemsbifurcationsphase flowisotropic oscillatorsHopf coordinatesperturbed elliptic oscillator

Mathematics Subject Classification ID

Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (21)

Numerical computation of incomplete elliptic integrals of a general form ⋮ Escapes in Hamiltonian systems with multiple exit channels. II ⋮ Periodic solutions of a galactic potential ⋮ A Hopf variables view on the libration points dynamics ⋮ An energy-momentum map for the time-reversal symmetric 1:1 resonance with \(\mathbb Z_2{\times}\mathbb Z_2\) symmetry ⋮ Universal unfolding of symmetric resonances ⋮ The Lissajous transformation. III: Parametric bifurcations ⋮ New families of periodic orbits for a galactic potential ⋮ CONNECTING SYMMETRIC AND ASYMMETRIC FAMILIES OF PERIODIC ORBITS IN SQUARED SYMMETRIC HAMILTONIANS ⋮ Quadratic Hamiltonians on non-symmetric Poisson structures ⋮ Structure of the centre manifold of the \(L_1\), \(L_2\) collinear libration points in the restricted three-body problem ⋮ The Hénon and Heiles Problem in Three Dimensions. ⋮ Extended Lissajous variables for oscillators in resonance. ⋮ Magnetic confinement of a neutral atom in a double-wire waveguide: a nonlinear dynamics approach ⋮ On the existence of chaotic circumferential waves in spinning disks ⋮ Normalization and the detection of integrability: The generalized van der Waals potential ⋮ Armbruster – Guckenheimer – Kim Hamiltonian System in $\bs 1$:$\bs 1$ Resonance ⋮ Periodic orbits for the generalized Yang-Mills Hamiltonian system in dimension 6 ⋮ On perturbed oscillators in 1-1-1 resonance: The case of axially symmetric cubic potentials ⋮ Escapes in Hamiltonian systems with multiple exit channels. I ⋮ Oscillators in resonance \(p\):\(q\):\(r\)

Cites Work

• The Lissajous transformation. III: Parametric bifurcations
• A mapping for the study of the 1/1 resonance in a galactic type Hamiltonian
• Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
• Canonical transformations depending on a small parameter
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