Abstract
The particular version of the inverse problem of dynamics considered here is: given the ‘slope function’ \(\gamma =f_{y}/f_{x}\), representing uniquely a family of planar curves \(f(x,y)=c\), find, if possible, potentials of the form \(V(x,y)=v(\gamma(x,y))\) which give rise to this family. Such potentials \(V\) will then have as equipotential curves the isoclinic curves \(\gamma\)=const of the family \(f(x,y)=c\). We show that, for the problem of admitting a solution, a necessary and sufficient condition must be satisfied by the given \(\gamma (x,y)\). Inferring by reasoning from particular to more general forms, we find analytically a very rich set of slope functions \(\gamma (x,y)\) satisfying this condition. In contrast to the (not always solvable) general case \(V=V(x,y)\), in all these cases we can find the potential \(v=v(\gamma)\) analytically by quadratures. Several examples of pairs \((\gamma,v(\gamma))\) are presented.
Authors
Mira-Cristiana Anisiu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
George Bozis
University of Thessaloniki, Department of Theoretical Mechanics, Thessaloniki, Greece
Keywords
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Paper coordinates
G. Bozis, M.-C. Anisiu, A solvable version of the inverse problem of dynamics, , http://doi.org/10.1088/0266-5611/21/2/005
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About this paper
Journal
Inverse problem
Publisher Name
IOPscience
DOI
Print ISSN
1361-6420
Online ISSN
0266-5611
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