A criterion for asymptotic straightness of force fields

Jürgen Scheurle; Stephan Schmitz

doi:10.3934/dcdsb.2010.14.777

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2010, Volume 14, Issue 2: 777-792. Doi: 10.3934/dcdsb.2010.14.777

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A criterion for asymptotic straightness of force fields

Jürgen Scheurle^1, and
Stephan Schmitz^1,

1.
Technische Universität München, Zentrum Mathematik, Boltzmannstraße 3, D-85748 Garching

Received: August 2009

Revised: January 2010

Published: September 2010

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Abstract

We consider the equations of motion arising from the classical scattering problem for potentials decreasing sufficiently fast at infinity. It is common to impose some conditions on the potential which guarantee that the paths of particles moving to infinity have straight lines as asymptotes. In this paper a new criterion is given by which one can decide whether or not a given potential has this special property called asymptotic straightness.

Keywords:

Classical particle scattering,
classical mechanics.

Mathematics Subject Classification: Primary: 37N05.

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