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

Wronskian method for bound state central force problem

2014 ◽  
Vol 35 (3) ◽  
pp. 035024
Author(s):  
Reginald Christian S Bernardo ◽  
Caesar P Palisoc
Keyword(s):  
Bound State ◽  
Central Force ◽  
Force Problem
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