Bifurcations of triple-periodic orbits

Details Bifurcations of triple-periodic orbits Bifurcations of triple-periodic orbits

Nov 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..22..403c&link_type=abstract

Celestial Mechanics, vol. 22, Nov. 1980, p. 403-413.

Computer Science

Numerical Analysis

12

Branching (Mathematics), Orbit Calculation, Orbital Mechanics, Periodic Variations, Equations Of Motion, Hamiltonian Functions, Invariance, Numerical Analysis, Perturbation Theory, Resonance, Symmetry, Variational Principles

Scientific paper

Families of periodic orbits in potentials symmetric with respect to the x-axis are considered. The characteristics of triple-periodic orbits (i.e. orbits intersecting the x-axis three times) that bifurcate from the central characteristic do not have their maximum or minimum energy (or perturbation) at the point of intersection. It is explained theoretically that this happens only for triple-periodic orbits and not for any other type of resonant periodic orbits and this fact is verified by numerical calculations.

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