  We use quasiclassical methods of superconductivity to study the
superconducting proximity effect from a topological $p$-wave superconductor
into a disordered one-dimensional metallic wire. We demonstrate that the
corresponding Eilenberger equations with disorder reduce to a closed non-linear
equation for the superconducting component of the matrix Green's function.
Remarkably, this equation is formally equivalent to a classical mechanical
system (i.e., Newton's equations), with the Green function corresponding to a
coordinate of a fictitious particle and the coordinate along the wire
corresponding to time. This mapping allows to obtain exact solutions in the
disordered nanowire in terms of elliptic functions. A surprising result that
comes out of this solution is that the $p$-wave superconductivity
proximity-induced into the disordered metal remains long-range, decaying as
slowly as the conventional $s$-wave superconductivity. It is also shown that
impurity scattering leads to the appearance of a zero-energy peak.
