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Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity

Bartuccelli, M, Deane, JHB and Gentile, G (2017) Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity Celestial Mechanics and Dynamical Astronomy, 128 (4). pp. 453-473.

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We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is C1 in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation for devising a fast algorithm for its solution comes from the desire to estimate probability of capture in various solutions, via Monte Carlo simulation: the integration times are very long, since we are interested in phenomena occurring on timescales of the order of 106{ 107 years. The proposed algorithm is based on the High-order Euler Method (HEM) which was described in [Bartuccelli et al. 2015], and it requires computer algebra to set up the code for its implementation. The pay-o is an overall increase in speed by a factor of about 7:5 compared to standard numerical methods. Means for accelerating the purely numerical computation are also discussed.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Gentile, G
Date : 13 March 2017
DOI : 10.1007/s10569-017-9760-1
Copyright Disclaimer : © The Author(s) 2017. This article is published with open access at
Uncontrolled Keywords : s Fast numerics for ODEs · Spin-orbit problem · Probability of capture · Monte Carlo simulation
Depositing User : Symplectic Elements
Date Deposited : 15 Feb 2017 12:46
Last Modified : 11 Jun 2019 12:04

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