Synchronization of perturbed non-linear Hamiltonians

Details Synchronization of perturbed non-linear Hamiltonians Synchronization of perturbed non-linear Hamiltonians

Apr 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..55..331m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 55, no. 4, p. 331-350.

Mathematics

1

Hamiltonian Functions, Nonlinear Equations, Orbits, Perturbation Theory, Synchronism, Elliptic Functions, Hyperbolic Trajectories, Kinetic Energy, Polynomials, Transformations (Mathematics)

Scientific paper

A new method for simplifying perturbed Hamiltonians in one DOF is proposed. A Lie simplification is used to eliminate all terms from the perturbation which are not of the same form as those already in the principal part. What remains of the perturbation can be collapsed into the main part by altering the coefficients; the simplification replaces the perturbed system with a modified version of the principal part. The second step then establishes the time transformation. The strategy is demonstrated by applying it in detail to a perturbed Duffing oscillator.

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