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Logarithmic Potential for a Flat Galaxy Model

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The potential field of a flat galaxy can be modeled using a logarithmic potential. Depending on the initial conditions, trajectories can resemble loops or two-dimensional harmonic oscillators.

Contributed by: Enrique Zeleny (June 2013)
Open content licensed under CC BY-NC-SA

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The Hamiltonian for a star moving in this potential is

,

where is the position in the galactic plane, and are the momentums, and and are parameters.

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