Classical Motion and Phase Space for a Harmonic Oscillator

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration illustrates the classical harmonic motion of a particle governed by the Hamiltonian , where the scaled variables are defined as
,
. 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 in the potential; (2) the phase space trajectory; and (3) the time series of
and
. In the upper two panels, the points with minimum (turning points) and maximum momentum are labeled with blue and green
's, respectively.
Contributed by: Porscha McRobbie and Eitan Geva (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
detailSectionParagraphPermanent Citation
"Classical Motion and Phase Space for a Harmonic Oscillator"
http://demonstrations.wolfram.com/ClassicalMotionAndPhaseSpaceForAHarmonicOscillator/
Wolfram Demonstrations Project
Published: March 7 2011