For animation, the program uses Matlab's normal plot command combined with the drawnow command. It is based on the ode45 solution of the corresponding differential equations.
Comprehensive documentation is provided, including a sketch of the most important steps of how to derive the equations of motion. A simple Mathematica notebook contains all of the manipulations.
This program won the File Exchange Pick of the Week.
This program visualizes the motion of a Cardan-mounted Euler top. It is helpful for analysing the transition from regular (oscillating) to irregular (chaotic) motion. The videos below show both types of motion, starting from similar initial value parameters.
Although the program feeds on data obtained from Mathematica and C, all of the visualisation algorithms are written in Matlab.
The 3D animation is created using the surf and drawnow commands. Example animation files are also provided. The rotation is based on Euler/Cardan angles and performed with individually computed rotation matrices (rather than using Matlab's own rotate algorithm).
The title of my Bachelor's thesis is: Melnikov's Method and the transition to chaotic behaviour in Cardan-mounted Euler tops.
Euler's top is a rigid body (with arbitrary shape, say, a potato) suspended from its centre of gravity (CoG). Its motion is regular and well-known. In most cases, however, the CoG cannot be reached by a regular suspension method like a thread or rod (one would have to reach inside the potato, i.e. pierce a hole through it). But the problem can be solved using a more sophisticated suspension mechanism: a 'Cardan mounting' (e.g. helicopters or gyro compasses are similar to Cardan-mounted rigid bodies).
But as the dynamic properties of the Cardan-mounted Euler top are different from those of the normal Euler top, the resulting motion is much more complex: the spectrum of possible motion ranges from regular (i.e. harmonic, predictable) to chaotic (i.e. unpredictable) in a multitude of varying degrees. My thesis provides a description of the transition from regular to chaotic motion, using methods from nonlinear dynamics and Melnikov's Method from perturbation theory. The resulting study reveals new aspects of the dynamics of both the unperturbed (regular) and the perturbed (chaotic) system. An animated visualisation can be viewed on the airlich frontpage.
Frei nach dem Tutorial auf 3DBuzz.com habe ich die Geometrie einer Unreal-Tournament-Map entwickelt. Die Belichtung und Texturierung sind zugegebenermaßen spärlich, aber die Geometrie ist dafür cool (auch wenn sie sich sicher nicht mit Klassikern wie DM-Fractal messen kann). Dazu habe ich noch einen Film mit UnrealED/Matinee gebastelt, der einen Rundflug um die Map zeigt.
