The 1:1 resonance in galactic-type Hamiltonian systems

Details The 1:1 resonance in galactic-type Hamiltonian systems The 1:1 resonance in galactic-type Hamiltonian systems

Jan 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...267..388c&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 267, no. 2, p. 388-391.

Astronomy and Astrophysics

Astrophysics

12

Elliptical Orbits, Harmonic Oscillation, Orbital Mechanics, Stellar Orbits, Equations Of Motion, Hamiltonian Functions

Scientific paper

The position and frequency of the 1:1 resonant periodic orbits in galactic type, 2D Hamiltonian systems, made up of harmonic oscillators with only one coupling term of a general form are found, using a semianalytical method. There are two types of resonant periodic orbits: (i) two straight lines going through the origin and (ii) two near ellipses traversed in opposite directions about the origin. The first type is found directly from the equations of motion while the second type is obtained using the equations of motion together with the averaged Hamiltonian. The results are compared with the outcomes of the numerical integration of the equations of motion, and the agreement is good.

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