On the motion under focal attraction in a rotating medium

TL;DR

This paper analyzes the phase portraits and bifurcations of a kinematic model related to focal attraction in a rotating medium, extending previous results to enhance understanding of its applicability.

Contribution

It provides a new, comprehensive study that extends Wilson's earlier work, offering essential insights into the model's behavior and applicability.

Findings

New phase portrait classifications

Bifurcation analysis results

Extended applicability conditions

Abstract

New results are established here on the phase portraits and bifurcations of the kinematic model in a system of ODE's, first presented by H.K. Wilson in his 1971 book, and by him attributed to L. Markus (unpublished). A new, self-sufficient, study which extends Wilson's result and allows an essential conclusion for the applicability of the model is reported here.