On the stable solutions to the rotating wire system

Simulation of the generalized rotating wire system with frictionless beads. Four beads are each treated as a one degree of freedom non-autonomous Hamiltonian system. They are non-autonomous because the Hamiltonian is generally not constant, although there is no explicit time dependence for the case where the angular velocity is constant. The system is generalized because the Hamiltonian is valid for any 3D wire and for any variable angular velocity.

The system is simulated for four beads on wires with different offset in the z-direction. The wires include various parabolic curves, lines and circles and depict stable solutions for Hamilton's equations and the beads' behavior in phase space displayed in the background canvas.

0:00 rotating parabolic wire
1:18 line wire
1:37 circle wire
1:56 oscillating angular velocity

Smooth transitions between zero and non-zero angular velocity was achieved using the up(x) function

The system was simulated using high order explicit symplectic integrators and was rendered in real time.

🎵 "fluid combustion" by "Synthetique" | not affiliated with/endorsed by.

Тэги:

#rotating_wire #bead_system #lagrangian #hamiltonian #rotating_beads_system #stable_solution #stable_equilibrium #classical_mechanics #angular_velocity #centrifugal #centripetal #bead_dynamics #dynamical_system

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