Abstract
It is shown that all planar potentials V(x, y) that can give rise, among other conditions, to monoparametric families of straight lines (FSL) satisfy a condition, expressed in the form of a second order nonlinear partial differential equation in V. To each such potential there corresponds just one FSL, whereas each preassigned monoparametric FSL can be created by infinitely many potentials. Various types of potentials (e.g., separable, homogeneous, etc.) producing FSL are studied. A necessary and sufficient condition is found, satisfied by all “adelphic” families of orbits, i.e. families that can coexist with a given FSL.
Authors
George Bozis
Department of Physics, University of Thessaloniki GR-54006 Thessaloniki, Greece
Mira-Cristiana Anisiu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Keywords
Inverse Problem of Dynamics; Planar Potentials; Families of Straight Lines
Paper coordinates
G. Bozis, M.-C. Anisiu, Families of straight lines in planar potentials, Rom. Astron. J. 11 (1) (2001), 27-43
About this paper
Journal
Romanian Astronomical Journal
Publisher Name
Romanian Academy
DOI
Print ISSN
1220-5168
Online ISSN
2285-3758 /2012
google scholar link
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