Geza Geleji

Simulation of Newtonian mechanics on a square piece of cloth made of a light and elastic material, suspended from its top two corners which are periodically brought closer to, then further away from one another.

The initial bounces caused by a drop from an unstable position are eventually replaced by smooth transitions to and from the two alternating states of the system as defined by the relative positions of the top two corners.

We approximate the solution to a system of first-order ordinary differential equations describing the movement of the particles making up the cloth using the classic Runge–Kutta method.

Visualization of the solution presented in [1, Section 2.1] to a special case of the Shallow water equations (inspired by the similar animations appearing therein). We made use of both an exact solution as well as an asymptotic approximation.

We simulate the behavior of three droplets falling into a liquid in a square tub with reflecting walls and no attennuation. The superposition of the reflected waves eventually causes the surface to behave in an apparently chaotic manner, with the original circular wavefronts progressively becoming more and more difficult to identify.

[1] Carrier, G. F.; Yeh, H. (2005), "Tsunami propagation from a finite source", Computer Modelling in Engineering & Sciences, 10 (2): 113–122, doi:10.3970/cmes.2005.010.113

(Please note that the animations appearing in this page are entirely my work and are in the public domain. You may use them in any way you like; no attribution is required.)