  The validity of Sundman-type asymptotic estimates for collision solutions is
established for a wide class of dynamical systems with singular forces,
including the classical $N$--body problems with Newtonian, quasi--homogeneous
and logarithmic potentials. The solutions are meant in the generalized sense of
Morse (locally --in space and time-- minimal trajectories with respect to
compactly supported variations) and their uniform limits. The analysis includes
the extension of the Von Zeipel's Theorem and the proof of isolatedness of
collisions. Furthermore, such asymptotic analysis is applied to prove the
absence of collisions for locally minimal trajectories.

Dynamical Systems;Classical Analysis and ODEs