  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.
