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March 27th, 2010, 05:14 PM   #1
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Composition

The phase flow is the one-parameter group of transformations of phase space

{\bf{p}(0),{\bf{q}(0))\longmapsto({\bf{p}(t), {\bf{q}(t))" />,

where and are solutions of the Hamilton's system of equations corresponding to initial condition and .

Show that is a group.


Can anyone help me prove the composition?
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June 24th, 2010, 08:39 AM   #2
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Re: Composition

Hallo, nice to meet you.
I'm new in here.

I think we could prove composition by the fact that the evolution of the system is uniquely determined by the initial conditions, hence applying gt1 on gt2 is the same as to take (q(t1),p(t1)) as initial condition.

See you.
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