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

A criterion for asymptotic straightness of force fields

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.
Citation: Jürgen Scheurle, Stephan Schmitz. A criterion for asymptotic straightness of force fields. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 777-792. doi: 10.3934/dcdsb.2010.14.777
[1]

Eliot Fried. New insights into the classical mechanics of particle systems. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1469-1504. doi: 10.3934/dcds.2010.28.1469

[2]

Jean-Claude Zambrini. Stochastic deformation of classical mechanics. Conference Publications, 2013, 2013 (special) : 807-813. doi: 10.3934/proc.2013.2013.807

[3]

Jamie Cruz, Miguel Gutiérrez. Spiral motion in classical mechanics. Conference Publications, 2009, 2009 (Special) : 191-197. doi: 10.3934/proc.2009.2009.191

[4]

Cristina Stoica. An approximation theorem in classical mechanics. Journal of Geometric Mechanics, 2016, 8 (3) : 359-374. doi: 10.3934/jgm.2016011

[5]

Rémi Lassalle, Jean Claude Zambrini. A weak approach to the stochastic deformation of classical mechanics. Journal of Geometric Mechanics, 2016, 8 (2) : 221-233. doi: 10.3934/jgm.2016005

[6]

Giuseppe Marmo, Giuseppe Morandi, Narasimhaiengar Mukunda. The Hamilton-Jacobi theory and the analogy between classical and quantum mechanics. Journal of Geometric Mechanics, 2009, 1 (3) : 317-355. doi: 10.3934/jgm.2009.1.317

[7]

Martin Frank, Thierry Goudon. On a generalized Boltzmann equation for non-classical particle transport. Kinetic & Related Models, 2010, 3 (3) : 395-407. doi: 10.3934/krm.2010.3.395

[8]

Julie Joie, Yifeng Lei, Marie-Christine Durrieu, Thierry Colin, Clair Poignard, Olivier Saut. Migration and orientation of endothelial cells on micropatterned polymers: A simple model based on classical mechanics. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1059-1076. doi: 10.3934/dcdsb.2015.20.1059

[9]

Claude Bardos, Nicolas Besse. The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits. Kinetic & Related Models, 2013, 6 (4) : 893-917. doi: 10.3934/krm.2013.6.893

[10]

Pedro M. Jordan. Finite-amplitude acoustics under the classical theory of particle-laden flows. Evolution Equations & Control Theory, 2019, 8 (1) : 101-116. doi: 10.3934/eect.2019006

[11]

Marco Castrillón López, Mark J. Gotay. Covariantizing classical field theories. Journal of Geometric Mechanics, 2011, 3 (4) : 487-506. doi: 10.3934/jgm.2011.3.487

[12]

María José Beltrán, José Bonet, Carmen Fernández. Classical operators on the Hörmander algebras. Discrete & Continuous Dynamical Systems - A, 2015, 35 (2) : 637-652. doi: 10.3934/dcds.2015.35.637

[13]

Claude Bardos, François Golse, Peter Markowich, Thierry Paul. On the classical limit of the Schrödinger equation. Discrete & Continuous Dynamical Systems - A, 2015, 35 (12) : 5689-5709. doi: 10.3934/dcds.2015.35.5689

[14]

Rabah Amir, Igor V. Evstigneev. A new perspective on the classical Cournot duopoly. Journal of Dynamics & Games, 2017, 4 (4) : 361-367. doi: 10.3934/jdg.2017019

[15]

Ruikuan Liu, Tian Ma, Shouhong Wang, Jiayan Yang. Thermodynamical potentials of classical and quantum systems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1411-1448. doi: 10.3934/dcdsb.2018214

[16]

Christopher M. Kellett. Classical converse theorems in Lyapunov's second method. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2333-2360. doi: 10.3934/dcdsb.2015.20.2333

[17]

Eduardo Martínez. Classical field theory on Lie algebroids: Multisymplectic formalism. Journal of Geometric Mechanics, 2018, 10 (1) : 93-138. doi: 10.3934/jgm.2018004

[18]

David Ginzburg. Constructing automorphic representations in split classical groups. Electronic Research Announcements, 2012, 19: 18-32. doi: 10.3934/era.2012.19.18

[19]

Jiakun Liu, Neil S. Trudinger. On the classical solvability of near field reflector problems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 895-916. doi: 10.3934/dcds.2016.36.895

[20]

Harald Markum, Rainer Pullirsch. Classical and quantum chaos in fundamental field theories. Conference Publications, 2003, 2003 (Special) : 596-603. doi: 10.3934/proc.2003.2003.596

2017 Impact Factor: 0.972

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]