Abstract
The particular version of the inverse problem of dynamics considered here is: given the ‘slope function’ \(\U{3b3} =f_{y}/f_{x}\), representing uniquely a family of planar curves \(f(x,y)=c\), find, if possible, potentials of the form \(V(x,y)=v(\U{3b3} (x,y))\) which give rise to this family. Such potentials \(V\) will then have as equipotential curves the isoclinic curves \(\U{3b3} =\) constof 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 \(\U{3b3} (x,y)\). Inferring by reasoning from particular to more general forms, we find analytically a very rich set of slope functions \(\(\U{3b3} (x,y)\) 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(\U{3b3} )\) analytically by quadratures. Several examples of pairs \((\U{3b3} ,v(\U{3b3}))\) are presented.
Authors
Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
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Paper coordinates
George Bozis and Mira-Cristiana Anisiu, A solvable version of the inverse problem of dynamics, Published 1 February 2005 • 2005 IOP Publishing Ltd, , , http://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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