Hamiltonian Vector Field (Xh)
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Let F(r,p) be a function on the phase space. | Let F(r,p) be a function on the phase space. | ||
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dF/dt = (dF/dr)(dr/dt)+(dF/dp)(dP/dt) | dF/dt = (dF/dr)(dr/dt)+(dF/dp)(dP/dt) | ||
d/dt = (dr/dt)d/dr + (dp/dt)d/dp | d/dt = (dr/dt)d/dr + (dp/dt)d/dp | ||
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Rewriting with Hamilton's equations yields: | Rewriting with Hamilton's equations yields: | ||
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d/dt = (dH/dp)d/dr - (dH/dr)d/dp | d/dt = (dH/dp)d/dr - (dH/dr)d/dp | ||
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This is the Hamiltonian vector field Xh. It is dependent on the Hamiltonian function. | This is the Hamiltonian vector field Xh. It is dependent on the Hamiltonian function. | ||
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| + | (pg.67) | ||
Current revision as of 21:57, 2 May 2006
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.
(pg.67)
