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advanced_tools:symplectic_structure [2018/05/03 13:15] jakobadmin [Why is it interesting?] |
advanced_tools:symplectic_structure [2018/10/11 14:59] (current) jakobadmin [Concrete] |
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* [[http://math.mit.edu/~cohn/Thoughts/symplectic.html|Why symplectic geometry is the natural setting for classical mechanics]] by Henry Cohn | * [[http://math.mit.edu/~cohn/Thoughts/symplectic.html|Why symplectic geometry is the natural setting for classical mechanics]] by Henry Cohn | ||
* Chapter "[[https://link.springer.com/chapter/10.1007%2F978-1-4612-0189-2_3#page-1|Phase Spaces of Mechanical Systems are Symplectic Manifolds" in the book Symmetry in Mechanics]] by Stephanie Frank Singer | * Chapter "[[https://link.springer.com/chapter/10.1007%2F978-1-4612-0189-2_3#page-1|Phase Spaces of Mechanical Systems are Symplectic Manifolds" in the book Symmetry in Mechanics]] by Stephanie Frank Singer | ||
+ | * See also Chapter 1 in Principles Of Newtonian And Quantum Mechanics by Gosson | ||
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$$d^2 S = 0$$ | $$d^2 S = 0$$ | ||
- | everywhere—and this gives Hamilton’s equations and the [[equations:maxwell_relations|Maxwell relations]]. | + | everywhere—and this gives Hamilton’s equations and the [[formulas:maxwell_relations|Maxwell relations]]. |
<cite>https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/</cite> | <cite>https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/</cite> |