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Hamiltonian phase-space flow

What you are seeing: the orbits of Hamilton's equations in the (q,p)(q, p) plane. Click anywhere to release a tracer at (q0,p0)(q_0, p_0); the integrator steps in time and traces an orbit at constant energy H(q,p)H(q, p). For the pendulum, you can see librations (closed loops) below the separatrix E=1E = 1 and rotations (open curves) above.

Figure 1. Phase-space orbits and the flow field of a Hamiltonian.
system
show flow

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.