A note on a family of non-gravitational central force potentials in dimension one. (December 2017)

• Record Type: Journal Article
• Authors: Alvarez-Ramírez, M.; Corbera, M.; Cors, Josep M.; García, A.
• Is Part Of: Applied mathematics letters. Volume 74(2017:Dec.)
• Page Start: 74
• Page End: 78
• Publication Date: 2017-12
• Subjects: Singularities -- Collisions -- Non-gravitational interactions; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2017.04.020
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.