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Some Analytical Results in Dynamics of Spheroidal Galaxies
Authors:M A Jalali  Y Sobouti
Institution:(1) Institute for Advanced Studies in Basic Sciences, P.O. Box 45195‐159, Gava Zang, Zanjan, Iran
Abstract:The surfaces of section in a harmonic oscillator potential, perturbed by quartic terms, are obtained analytically. A succession of action‐angle, Lissajous and Lie transformations near the 1:1 commensurability, reduces the three‐dimensional motion to a one‐dimensional one. The latter is solved in terms of Jacobi's elliptic functions. Existence conditions for periodic orbits are found and two general families of such solutions are introduced. Two examples of regular motions in oblate and prolate spheroids are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.
Keywords:galactic dynamics  Lissajous transformation  elliptic functions
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