Two-dimension potentials which generate spatial families of orbits

Details Two-dimension potentials which generate spatial families of orbits Two-dimension potentials which generate spatial families of orbits

Apr 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009an....330..411a&link_type=abstract

Astronomische Nachrichten, Vol.330, Issue 4, p.411

Statistics

Applications

Celestial Mechanics, Stellar Dynamics

Scientific paper

We consider the following case of the 3D inverse problem of dynamics: Given a spatial two-parametric family of curves f(x,y,z)=c1, g(x,y,z)=c2, find possibly existing two-dimension potentials under whose action the curves of the family are trajectories for a unit mass particle. First we establish the conditions which must be fulfilled by the family so that potentials of the form w(y,z) give rise to the curves of the family, and we present some applications. Then we examine briefly the existence of potentials depending on (x,z), respectively (x,y), which are compatible with the given family.

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