From j0r1's page

Physics: Applets

Some applets

Well, currently only one applet...

Embedding a 2D metric in 3D Euclidean space

The following applet tries to embed a 2D metric in a 3D Euclidean space. More specifically, the 2D metric is of the following type:

dS² = dθ²+f(θ)²dφ² .

The applet lets you embed such a surface in a three-dimensional Euclidean space for different kinds of f(θ) definitions. Note that in the applet, the variable x is used instead of θ and that mathematical functions use the Java syntax: for example, use Math.sin(x) instead of sin(x).

Some interesting expressions to try are:

• Math.sin(x)*(1-0.75*Math.sin(x)*Math.sin(x)): this will draw a peanut-shaped surface (this is the default setting)
• Math.sin(x): this draws a sphere
• Math.sin(x)*(1+0.1*Math.sin(x)*Math.sin(x))
• 0.8*Math.sin(x)-0.1*Math.sin(x*2)

Spring pendulum

Governor