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The Monotonicity of the Apsidal Angle Using the Theory of Potential Oscillators

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Abstract

In a central force system the angle between two successive passages of a body through pericenters is called the apsidal angle. In this paper we prove that for central forces of the form \(f(r)\sim \lambda r^{-\,(\alpha +1)}\) with \(\alpha <2\) the apsidal angle is a monotonous function of the energy, or equivalently of the orbital eccentricity.

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Acknowledgements

The author want to thank Prof. Rafael Ortega for the fruitful discussions that led to the interpretation of the apsidal angle as the period function of an abstract oscillator. The author is partially supported by the MINECO Grant MTM2014-52209-C2-1-P and MEC/FEDER Grant MTM2014-52232-P.

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  1. Departamento de Matemática Aplicada, Universidad de Granada, Granada, Spain

    D. Rojas

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  1. D. Rojas
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Correspondence to D. Rojas.

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Rojas, D. The Monotonicity of the Apsidal Angle Using the Theory of Potential Oscillators. Qual. Theory Dyn. Syst. 17, 631–635 (2018). https://doi.org/10.1007/s12346-017-0265-9

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  • DOI: https://doi.org/10.1007/s12346-017-0265-9

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