Processing math: 100%

Posts by Mira Anisiu

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

Keywords

?

Paper coordinates

A solvable version of the inverse problem of dynamics, Inverse Problems, 21 (2005) no. 2, pp. 487-497, http://doi.org/10.1088/0266-5611/21/2/005

PDF

??

About this paper

Journal

Inverse problem

Publisher Name

IOPscience

DOI
Print ISSN

1361-6420

Online ISSN

0266-5611

google scholar link

Related Posts

PDES in the inverse problem of dynamics

AbstractAuthorsKeywordsReferencesPDF(pdf file here) Cite this paper as:Anisiu M.C., PDES in the inverse problem of dynamics, Analysis and Optimization of Differential Systems,…

Total palindrome complexity of finite words

AbstractAuthorsMira-Cristiana Anisiu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania Valeriu Anisiu Babeş-Bolyai University of Cluj-Napoca, Faculty of Mathematics and…