Abstract
Soon after establishing the famous properties of the 1∕r 2 law of force, Newton described a spiraling orbit of a particle under a central force in 1∕r 3. He also noticed that the addition of a force in 1∕r 3 to another force results in a kind of precession of the orbit, see [14, Book 1, Proposition 44]. In 1842, Jacobi [8] gave general results about the force fields which are homogeneous of degree − 3 and derived from a potential. More recently, Montgomery [12] gave an impressive description of the dynamics of the planar 3-body problem with a force in 1∕r 3. Such homogeneity of the force also appears in Appell’s projective dynamics, where the force is considered together with a constraint, see [2].
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Acknowledgements
This work benefited from discussions with Alexey Borisov, Alain Chenciner, Yuri Fedorov, Božidar Jovanović, Hans Lundmark and Ivan Mamaev.
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Albouy, A. (2015). On the Force Fields Which Are Homogeneous of Degree −3. In: Corbera, M., Cors, J., Llibre, J., Korobeinikov, A. (eds) Extended Abstracts Spring 2014. Trends in Mathematics(), vol 4. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-22129-8_1
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