Re: Newton Vs Lagrange Vs Hamilton
From: Arnold Neumaier (Arnold.Neumaier_at_univie.ac.at)
Date: 03/29/05
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Date: Tue, 29 Mar 2005 17:16:30 +0000 (UTC)
Neil Price wrote:
> vonnyn@hotmail.com (Vonny N) wrote in message news:<df799de5.0503251424.2f339940@posting.google.com>...
>
>>What is the relationship between:
>>
>>1. Newtonian Mechanics
>>2. Lagrangian Mechanics
>>3. Hamiltonian Mechanics
1 is a special case of 3 which is a special case of 2.
>>Can they be declared to be *rigorously* mathematically equivalent?
No.
> On the other hand, Hamiltonian mechanics is more directly amenable to
> techniques from symplectic geometry, e.g. symplectic reduction,
> definitions involving integrability, etc.
There is also a symplectic view of Lagrangian mechanics, presented,
e.g., in the book on Mechanics and Symmetry by Marsden and Ratiu.
>>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?
Marsden and Ratiu give an almost rigorous approach.
> See the book "foundations of mechanics" by Abraham and Marsden or
> "introduction to mechanics and symmetry" by Marsden and Ratiu.
Marsden and Ratiu give an almost rigorous approach.
Arnold Neumaier
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