A note on a family of non-gravitational central force potentials in dimension one

In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. We offer an altern...

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Bibliographic Details
Published in:Applied mathematics letters Vol. 74; pp. 74 - 78
Main Authors: Alvarez-Ramírez, M., Corbera, M., Cors, Josep M., García, A.
Format: Journal Article Publication
Language:English
Published: Elsevier Ltd 01.12.2017
Elsevier
Subjects:
70 Mechanics of particles and systems
70F Dynamics of a system of particles, including celestial mechanics
Celestial mechanics
Classificació AMS
Collisions
Collisions (Physics)
Col·lisions (Física)
Enginyeria mecànica
Matemàtiques i estadística
Mecànica celest
Non-gravitational interactions
Singularitats (Matemàtica)
Singularities
Singularities (Mathematics)
Àrees temàtiques de la UPC
Singularities
Non-gravitational interactions
Collisions
ISSN:0893-9659, 1873-5452
Online Access:Get full text
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Summary:In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. We offer an alternative point of view for the study for the motion of a system of two particles which will always move in some fixed line, we take R for the position space. If we fix the center of mass at the origin, the system reduces to that of a single particle of unit mass in a central force field. We take the potential energy function U(x)=|x|β, where x is the position of the single particle and β is some positive real number.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2017.04.020