Some Analytical Results in Dynamics of Spheroidal Galaxies |
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Authors: | M A Jalali Y Sobouti |
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Institution: | (1) Institute for Advanced Studies in Basic Sciences, P.O. Box 45195‐159, Gava Zang, Zanjan, Iran |
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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. |
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Keywords: | galactic dynamics Lissajous transformation elliptic functions |
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