One-dimensional central-force problem, including radiation reaction

1976 ◽  
Vol 14 (4) ◽  
pp. 939-944 ◽  
Author(s):  
John C. Kasher
Keyword(s):  
Radiation Reaction ◽  
Central Force ◽  
One Dimensional ◽  
Force Problem

scholarly journals The One-dimensional Coulomb-force Problem in Classical Radiation Reaction Theories

1977 ◽  
Vol 32 (7) ◽  
pp. 685-691
Author(s):  
W. Heudorfer ◽  
M. Sorg
Keyword(s):  
Coulomb Potential ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Coulomb Force ◽  
Stationary States ◽  
One Dimensional ◽  
The One ◽  
Force Problem ◽  
Classical Radiation

Abstract Numerical solutions of the recently proposed equations of motion for the classically radiating electron are obtained for the case where the particle moves in a one-dimensional Coulomb potential (both attractive and repulsive). The solutions are discussed and found to be meaningful also in that case, where the well-known Lorentz-Dirac equation fails (attractive Coulomb force). Discrete, stationary states are found in a non-singular version of the Coulomb potential. During the transition between those stationary states the particle looses energy by emission of radiation, which results in a smaller amplitude of the stationary oscillations.

Genericity of the non-periodic solutions of the central force problem

1990 ◽  
Vol 165 (1) ◽  
pp. 95-99
Author(s):  
Ana Nunes ◽  
Josefina Casasayas
Keyword(s):  
Periodic Solutions ◽  
Central Force ◽  
Force Problem

scholarly journals Symmetries in central-force problems

2003 ◽  
pp. 47-52 ◽  
Author(s):  
V. Mioc ◽  
M. Barbosu
Keyword(s):  
Vector Fields ◽  
Body Problem ◽  
Blow Up ◽  
Central Force ◽  
Polar Coordinates ◽  
Global Flow ◽  
Two Body Problem ◽  
Concrete Problem ◽  
Central Force Problems ◽  
Force Problem

The two-body problem in central fields (reducible to a central-force problem) models a lot of concrete astronomical situations. The corresponding vector fields (in Cartesian and polar coordinates, extended via collision-blow-up and infinity-blow-up transformations) exhibit nice symmetries that form eight-element Abelian groups endowed with an idempotent structure. All these groups are isomorphic, which is not a trivial result, given the different structures of the corresponding phase spaces. Each of these groups contains seven four-element subgroups isomorphic to Klein?s group. These symmetries are of much help in understanding various characteristics of the global flow of the general problem or of a concrete problem at hand, and are essential in searching for periodic orbits.

scholarly journals Exponential Stability in the Perturbed Central Force Problem

2018 ◽  
Vol 23 (7-8) ◽  
pp. 821-841
Author(s):  
Dario Bambusi ◽  
Alessandra Fusè ◽  
Marco Sansottera
Keyword(s):  
Exponential Stability ◽  
Central Force ◽  
Force Problem

scholarly journals Not-so-classical mechanics: unexpected symmetries of classical motion

2005 ◽  
Vol 83 (2) ◽  
pp. 91-138 ◽  
Author(s):  
James T Wheeler
Keyword(s):  
Gauge Theories ◽  
Vries Equation ◽  
Classical Mechanics ◽  
Logistic Equation ◽  
Central Force ◽  
Newtonian Mechanics ◽  
Classical Motion ◽  
Recent Interest ◽  
Bohmian Quantum Mechanics ◽  
Force Problem

A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central-force problem; inequivalent Lagrangians and Hamiltonians; constants of central-force motion; a general discussion of higher order Lagrangians and Hamiltonians, with examples from Bohmian quantum mechanics, the Korteweg–de Vries equation, and the logistic equation; gauge theories of Newtonian mechanics; and classical spin, Grassmann numbers, and pseudomechanics. PACS No.: 45.25.Jj

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