Alain Albouy - "Projective dynamics of a classical particle or a multiparticle system".

There exists a "projective dynamics of the particle", which underlies intrinsically the 
"classical particle dynamics", exactly as projective geometry underlies Euclidean geometry.  

In classical particle dynamics a particle moves in the Euclidean space subjected to a potential. 
In projective dynamics the position space has only the local structure of the real projective space, 
and a new object, the projective force, must be introduced.

These statements are direct consequences of Appell's remarks on the homography in mechanics, 
and are compatible with similar statements due to Tabachnikov concerning projective billiards.

We will review the successes of the projective point of view in the dynamics of a particle, 
trying to explain  briefly some results in
http://arxiv.org/abs/math-ph/0612031 and
http://arxiv.org/abs/math-ph/0501026 
or some results published by Alexey Borisov and Ivan Mamaev.