Classical Barrier Crossing and Phase Space

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This Demonstration illustrates the classical motion of a particle governed by the Hamiltonian . Here
and
are obtained by solving Hamilton's equations of motion, subject to the initial conditions
and
. The three panels animate synchronously: (1) the motion of the particle as it approaches the potential, (2) the phase space trajectory, and (3) the time series of
and
. In the upper two panels, the points with minimum momentum (turning points) are labeled with blue
's.
Contributed by: Porscha McRobbie and Eitan Geva (March 2011)
Open content licensed under CC BY-NC-SA
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"Classical Barrier Crossing and Phase Space"
http://demonstrations.wolfram.com/ClassicalBarrierCrossingAndPhaseSpace/
Wolfram Demonstrations Project
Published: March 7 2011