Phase space & Liouville's Theorem

Hamiltonian dynamics exists in phase space -- a space of formed of all the generalized positions and generalized momenta. We explore ways to solve Hamilton's equations in this space.
Music "Everything" by Vi Hart
/ vihartvihart

[@sdmcal4]

ung phys student here and I got your videos recommended to me from GT, I love the way you present this thank you for the effort you put in these videos.

[@MGB-wz3jz]

One point of critique, you show a phase space plot with spiralling motion. However, Hamiltonian systems never have a sink or source at a singularity. Great video nonetheless!

[@osmanhussein3893]

Wonderlful explanation. Very much appreciated!

[@kierkegaard54]

The "proof" given at 6:36 doesn't seem too convincing, at least visually I can imagine a lot of points outside A(t) where the trayectorias do not cross. Besides that, great video and a very good topic

[@eastofthegreenline3324]

Enjoyed this...at (e.g.) 9:10, why do you use cursive delta in the integral? At 8:17 also, dA = Int (n.v dt)dg and all the d's are cursive, like variational notation?

[@jennyone8829]

Thank you so much 🎈👽🪬☀️♾️

[@carolinaraquellagunarangel274]

Amazing thanks