Confined free motion under a dipole potential

Authors

  • R. Sánchez-Martinez Facultad de Fisica, Universidad Veracruzana,
  • H. N. Nuñez-Yepez Departamento de Fisica, Universidad Aut´onoma Metropolitana,
  • A. L. Salas-Brito Laboratorio de Sistemas Dinamicos, Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana,

DOI:

https://doi.org/10.31349/RevMexFisE.17.272

Keywords:

inverse square potential, equivalence to free motion, impenetrability of the origin

Abstract

The classical motion of a particle in a dipolar potential, $U_{\hbox{dip}}(q) = - {k}/{q^2}$, and free motion along a curve in phase space are proven to be equivalent. We also prove that the singularity at $q=0$ in the dipolar potential is strong enough as to prevent the flow of particles from one side of the singularity to the other. This effect does not depende on whether the dipole potential is regarded as attractive ($k>0$) or as repulsive ($k<0$). All the proofs are given using the Hamitonian formalism, therefore they may be used for illustrating the power the Hamiltonian approach may confer in analysing different mecanical systems. The discussion is keep within the reach of advanced undergraduate or graduate students of Hamiltonian mechanics.

Author Biography

R. Sánchez-Martinez, Facultad de Fisica, Universidad Veracruzana,

Departamento de Ciencias Básicas, Área de Física Teórica y Materia Condensada, Profesor Investigador Titular C

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Published

2020-07-01

How to Cite

[1]
R. Sánchez-Martinez, H. N. Nuñez-Yepez, and A. L. Salas-Brito, “Confined free motion under a dipole potential”, Rev. Mex. Fis. E, vol. 17, no. 2 Jul-Dec, pp. 272–275, Jul. 2020.

Issue

Vol. 17 No. 2 Jul-Dec (2020): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2020 A. L. Salas-Brito

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