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Particles Under a Central Force Field

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Mathematical Models with Singularities

Part of the book series: Atlantis Briefs in Differential Equations ((ABDE,volume 1))

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Abstract

A force field in \({\mathbb R}^N\) is called central or radially symmetric if its magnitude only depends on the distance to the origin and its direction is proportional to the vector position, that is, it always points to the origin. The study of a radially symmetric system is reduced to a second-order scalar equation with a repulsive singularity. We review some of the most interesting models with radial symmetry.

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Notes

  1. 1.

    The history of solar sails goes back at least to Kepler. Nowadays, NASA is actively working on the practical use of solar sailing in current space mission designs (see for example the NanoSail-D mission), with very positive results [24]. The use of solar sailing as an effective propulsion system for space travelling appears in many science-fiction books and films. Perhaps the most known author is Arthur C. Clarke, who has a nice story entitled “The Wind from the Sun”. As a concession to our freaky side, in the film series Star Trek we can find the Bajoran Lightship as a spacecraft propelled by sunlight, whereas in Stars Wars (Episode II), Count Dooku (better known as Darth Tyranus) owns a Punworcca 116-class interstellar solar sailer.

  2. 2.

    Other variants leading to the same model are plausible. In particular, on a solar sail we may control the effective cross section \(\sigma (t)\) as a function of time.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Granada, Granada, Spain

    Pedro J. Torres

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  1. Pedro J. Torres
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Correspondence to Pedro J. Torres .

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Torres, P.J. (2015). Particles Under a Central Force Field. In: Mathematical Models with Singularities. Atlantis Briefs in Differential Equations, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-106-2_4

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