Newton Vs Lagrange Vs Hamilton

From: Vonny N (vonnyn_at_hotmail.com)
Date: 03/25/05 

Date: Fri, 25 Mar 2005 22:54:41 +0000 (UTC)

What is the relationship between:

1. Newtonian Mechanics
2. Lagrangian Mechanics
3. Hamiltonian Mechanics

Can they be declared to be *rigorously* mathematically equivalent?

Does it suffice to say that they are reformulations of each other,
each well-adapted to a particular class of problems?

If so, can we describe reasonably clearly which type of problems are
more easily represented and/or solved using each version of mechanics?

Finally, is there a book on classical mechanics which treats all three
of these approaches to mechanics, along with their
inter-relationships, with mathematical rigour? (I'm afraid I don't
much like Goldstein's widely cited book).

Vonny N.