A note on a family of non-gravitational central force potentials in dimension one
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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|ß, where x is the position of the single particle and ß is some positive real number.
CitationAlvarez-Ramírez, M., Corbera-Subirana, M., Cors, J., García, A. A note on a family of non-gravitational central force potentials in dimension one. "Applied mathematics letters", 1 Desembre 2017, vol. 74, p. 74-78.