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September  2010, 14(2): 777-792. doi: 10.3934/dcdsb.2010.14.777

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, Germany, Germany

Received  August 2009 Revised  January 2010 Published  June 2010

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 mechanics., Classical particle scattering.
Mathematics Subject Classification: Primary: 37N0.
Citation: Jürgen Scheurle, Stephan Schmitz. A criterion for asymptotic straightness of force fields. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 777-792. doi: 10.3934/dcdsb.2010.14.777
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