Polynomial approximations of Poincare maps for Hamiltonian systems, 2

Details Polynomial approximations of Poincare maps for Hamiltonian systems, 2 Polynomial approximations of Poincare maps for Hamiltonian systems, 2

Feb 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...282..291p&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 282, no. 1, p. 291-303

Astronomy and Astrophysics

Astrophysics

3

Approximation, Astronomical Maps, Hamiltonian Functions, Interpolation, Orbital Mechanics, Poincare Spheres, Polynomials, Three Body Problem, Liapunov Functions, Series Expansion, Taylor Series, Trajectory Analysis

Scientific paper

In Paper 1 polynomial interpolating formula of order 3 and 5 have been proposed and tested for transforming a non-linear differential Hamiltonian system into a map without having to integrate whole orbits as in the well known Poincare return map technique. The precision of the computations increases drastically with the order of the polynomial fit which requires an extended amount of local formation, i.e. information about neighboring points. The first part of the paper deals with another type of interpolation where the information, within the same accuracy, refers only to the nearest neighbors but takes into account gradient information. The results are in very good agreement with those obtained using an order 3 symmetrical interpolation formula well inside the phase space. Moreover the new method is more effective at the border of the phase space when compared with asymmetrical interpolation. The second part of the paper deals with higher dimensional mappings, i.e. mappings for Hamiltonian systems with 3 degrees of freedom.

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