Hamiltonian Vector Field (Xh)

From Vectorcalcumb

Let F(r,p) be a function on the phase space.

dF/dt = (dF/dr)(dr/dt)+(dF/dp)(dP/dt) d/dt = (dr/dt)d/dr + (dp/dt)d/dp

Rewriting with Hamilton's equations yields:

d/dt = (dH/dp)d/dr - (dH/dr)d/dp This is the Hamiltonian vector field Xh. It is dependent on the Hamiltonian function.