Скачать с ютуб Beads on a rotating platform в хорошем качестве

Beads on a rotating platform

Simulation of frictionless two-bead dynamical systems. The beads move along a knot, ellipse or a parabolic curve, which are connected to a common platform with a small moment of inertia. The systems have two degrees of freedom disregarding the third cyclic coordinate associated with the rotation of the platform that has a constant conjugate momentum. The system dynamics is generally governed by conservation of angular momentum. The bead coordinates (q1,q2) are tracked on the background canvas, hinting either regular or chaotic motion. 0:00 two parabolas (regular) 0:12 two parabolas (chaotic) 0:26 parabola and trefoil knot (regular) 0:38 parabola and trefoil knot (regular) 0:44 parabola and trefoil knot (regular) 0:51 parabola and trefoil knot (regular) 1:04 parabola and trefoil knot (chaotic) 1:36 ellipse and square knot (regular) 1:48 ellipse and square knot (regular) 1:55 ellipse and square knot (chaotic) 2:07 ellipse and granny knot (chaotic) 2:46 ellipse and granny knot (regular) The Hamiltonian of the system was derived in its most general for applicable for N beads of different masses on any N smooth curves provided for each the path and its first two first derivatives in parametric form. The simulation was performed using high order explicit symplectic integrators and was rendered in real time. 🎵 "Oldskool again!" by "Borgert" | not affiliated with/endorsed by.