On Fri, 18 Jul 2008, Markus Frank wrote:

I am looking for any reference (article, textbook, etc.) that explains the
transition from classical continuum mechanics to classical point mechanics
(i.e. Newton, Lagrange or Hamilton) in *this* direction. This would likely
mean starting from the differential conservation laws of continuum mechanics
for mass, momentum and energy and somehow modeling the respective densities
and currents by a sum of Dirac delta functions for each particle. I have some
ideas how to do this on my own but would like to have an "authoritative"
reference to back it up.

Depending on what you mean, it isn't so easy. Sure, you can model a rigid
body moving through a fluid or vacuum using classical continuum mechanics,
but this is very complicated. Why? For starters, the properties of the
continuum are time-dependent (the object moves, so the properties of the
medium at a point that the object moves through go from vacuum (or fluid)
- object - vacuum).

This isn't likely to lead to any analytical solution (sure, it could be
done by computational brute force, but that's not what you're after, is
it?), so don't expect anything in the old literature.

It's an interesting problem, but time-dependent constitutive equations
make it nasty. Please, let us know about your ideas on this!

--
Timo