Conservative fields derived from two monoparametric families of planar orbits

Details Conservative fields derived from two monoparametric families of planar orbits Conservative fields derived from two monoparametric families of planar orbits

Apr 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985a%26a...145..215b&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 145, no. 1, April 1985, p. 215-220.

Astronomy and Astrophysics

Astrophysics

6

Celestial Mechanics, Orbital Mechanics, Astrodynamics, Curves (Geometry), Partial Differential Equations, Potential Fields

Scientific paper

With the aid of Szebehely's partial differential equation for the inverse problem in dynamics, the authors prove that, in general, two preassigned monoparametric families of planar curves f(x, y) = c1 and g(x, y) = c2 are not compatible, i.e., there does not exist a potential field U = U(x, y) which can generate both these families. Only if the given functions f(x, y) and g(x, y) satisfy a certain condition, the families are compatible. The corresponding potential field, as well as the total energies along each orbit, are, in general, determined uniquely, apart from a multiplicative and an additive constant. In some special cases, up to three additional arbitrary constants may enter into the expression for the potential.

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