Prerequisite: Di ff erent types of constraints, Virtual displacement and virtual work, D'Alembert's

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Classical Mechanics
Prerequisite: Di
ff
erent types of constraints, Virtual displacement and virtual work, D'Alembert's
principle, generalized co-ordinates and momenta
In this course, we will start from the principle of stationary action (variational principle).
Textbooks:
1. Goldstein 2. Taylor
3. Greiner

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Liouville's theorem does not imply that every point along a given path has the same 
density. In other words, suppose that two particles, A and B, follow the same trajectory, 
except that particle A leads particle B by a 
fi
nite time (or equivalently, there is a 
fi
nite 
distance in phase space between the two particles). Particle A could be in a region of 
di
ff
erent density than particle B.
Liouville's theorem only holds in the limit that the particles are in
fi
nitely close together. 
Equivalently, Liouville's theorem does not hold for any ensemble that consists of a 
fi
nite 
number of particles; instead the theorem describes the probability density in phase space 
of an ensemble consisting of an in
fi
nite number of possible states.

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