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Motion on a given surface: potentials producing geodesic lines as trajectories

Kotoulas, Thomas A. (2006) Motion on a given surface: potentials producing geodesic lines as trajectories. Rendiconti del Seminario della Facoltà di Scienze dell'Università di Cagliari, 76 (1-2). pp. 1-15. ISSN 0370727X

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Abstract

In the light of inverse problem of dynamics, we consider the motion of a material point on an arbitrary two-dimensional surface, submersed in OE3. We study twodimensional potentials which produce a mono-parametric family of geodesic lines as trajectories. We establish a new, non-linear partial differential condition for the potential function V = V(u, v). With the aid of this condition, we examine if a given potential produces a family of geodesic lines on a certain surface or not. On the other hand, we can check if a given family of regular orbits is indeed a family of geodesic lines on a certain surface and then find the potential function V = V(u, v) which gives rise to this family of orbits. Special cases are also studied and pertinent examples are worked out.

Item Type:Article
Date:2006
Institution:Universita' degli Studi di Cagliari
Divisions:Centri > Seminario Scientifico della Facolta' di Scienze MM.FF.NN.
Subjects:Area 02 - Scienze fisiche > FIS/02 Fisica teorica, modelli e metodi matematici
Uncontrolled Keywords:Motion on a surface, Mono-parametric families of orbits, Potentials,Lagrangian Mechanics
ID Code:69
Deposited On:29 Oct 2008 10:28

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