Solution of the Three-Dimensional Inverse Problem

Details Solution of the Three-Dimensional Inverse Problem Solution of the Three-Dimensional Inverse Problem

Apr 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..38..357b&link_type=abstract

Celestial Mechanics, Volume 38, Issue 4, pp.357-375

Physics

12

Scientific paper

The three dimensional inverse problem for a material point of unit mass, moving in an autonomous conservative field, is solved. Given a two-parametric family of space curves f(x,y,z) = c1, g(x,y,z) = c2, it is shown that, in general, no potential U = U(x,y,z) exists which can give rise to this family. However, if the given functions f(x,y,z) and g(x,y,z) satisfy certain conditions, the corresponding potential U(x,y,z), as well as the total energy E = E(f,g) are determined uniquely, apart from a multiplicative and an additive constant.

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