Sundman transformation and alternative tangent structuresSundman transformation and alternative tangent structures
arXiv:2304.00284 · doi:10.1088/1751-8121/acc913
Abstract
A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function defining the Sundman transformation is shown. Among other applications of such theory we study the linearisability of a system of second-order differential equations and in particular the simplest case of a second-order differential equation. The theory is illustrated with several examples.
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