- #1
CrazyNeutrino
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What is a symplectic manifold or symplectic geometry? (In intuitive terms please)
I have a vague understanding that it involves some metric that assigns an area to a position and conjugate momentum that happens to be preserved. What is 'special' about Hamilton's formulation that makes it more useful than Lagrange's? Why is it that phase space has this special geometry but state space does not? What makes the generalized momentum a more useful coordinate than the generalized velocity?
I have a vague understanding that it involves some metric that assigns an area to a position and conjugate momentum that happens to be preserved. What is 'special' about Hamilton's formulation that makes it more useful than Lagrange's? Why is it that phase space has this special geometry but state space does not? What makes the generalized momentum a more useful coordinate than the generalized velocity?