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--- theories:classical_mechanics:hamiltonian [2018/05/06 11:32]
jakobadmin [Concrete]
+++ theories:classical_mechanics:hamiltonian [2018/05/13 09:17]
jakobadmin ↷ Links adapted because of a move operation
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 a ‘Hamiltonian’ $$H : T^* Q \to \mathbb{R}$$ or a ‘Lagrangian’ $$L : T Q \to \mathbb{R}$$
-Instead, we started with Hamilton’s principal function $$S : Q \to \mathbb{R}$$ where $Q$ is not the usual configuration space describing possible positions for a particle, but the ‘extended’ configuration space, which also includes time. Only this way do Hamilton’s equations, like the [[equations:maxwell_relations|Maxwell relations]], become a trivial consequence of the fact that partial derivatives commute.
+Instead, we started with Hamilton’s principal function $$S : Q \to \mathbb{R}$$ where $Q$ is not the usual configuration space describing possible positions for a particle, but the ‘extended’ configuration space, which also includes time. Only this way do Hamilton’s equations, like the [[formulas:maxwell_relations|Maxwell relations]], become a trivial consequence of the fact that partial derivatives commute.
 <cite>https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/</cite>