A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case

Roberto Castelli

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arXiv · 1309.1594

A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case

Roberto Castelli

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Abstract

This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogenous potential of degree $-2\leq α\leq 1$ and logarithmic potential. We derive a formula for the apsidal angle as a fixed-end points integral and we study the derivative of the apsidal angle with respect to the angular momentum $\ell$. The monotonicity of the apsidal angle as function of $\ell$ is discussed and it is proved in the logarithmic potential case.

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Roberto Castelli. 2013-09-06. A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case. https://arxiv.org/abs/1309.1594

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