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

Roberto Castelli

doi:10.1016/j.jmaa.2013.12.035

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

Roberto Castelli^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogeneous potential of degree -2 ≤ α ≤ 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 ℓ. The monotonicity of the apsidal angle as function of ℓ is discussed and it is proved in the logarithmic potential case.

Original language	English
Pages (from-to)	727-751
Number of pages	25
Journal	Journal of Mathematical Analysis and Applications
Volume	413
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2013.12.035
Publication status	Published - 15 May 2014

Keywords

Apsidal angle
Logarithmic potential
Two-body problem

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10.1016/j.jmaa.2013.12.035

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abstract = "This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogeneous potential of degree -2 ≤ α ≤ 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 ℓ. The monotonicity of the apsidal angle as function of ℓ is discussed and it is proved in the logarithmic potential case.",

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AB - This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogeneous potential of degree -2 ≤ α ≤ 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 ℓ. The monotonicity of the apsidal angle as function of ℓ is discussed and it is proved in the logarithmic potential case.

KW - Apsidal angle

KW - Logarithmic potential

KW - Two-body problem

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

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

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