On closed but non-geometrically similar orbits

Details On closed but non-geometrically similar orbits On closed but non-geometrically similar orbits

Nov 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..96..311b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 96, Issue 3-4, pp. 311-316

Astronomy and Astrophysics

Astronomy

2

Closed Orbits, Similarity

Scientific paper

As is well known, the existence of geometrically similar orbits for a particle moving under a central conservative force is a consequence of the fact that the corresponding potential energy is a homogeneous function of the co-ordinates. In this paper, we consider a particular non-homogeneous potential of the form V = U + W, where U and W are homogenous functions of degrees -1 and -2, respectively, because, for this potential, the search of closed orbits, for discrete values of the angular momentum, is straightforward. We focus our attention on these daisy-like charming orbits and graphically show the consequences of the impossibility of geometrical similarity.

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