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I decided to try adding some moving things to this site to make it more of a quasi-static site.

I’ve added a new section called simulations; a very ambitious action, as though I intend to add more than what’s in there (I’m not sure that I do). Nonetheless, it has a little p5 js canvas thing I made that allows the user to play around with little planets, and see if they can get a stable solution for the 3 body problem!

In terms of the actual implementation, I decided to go with the straightforward approach.

The processing is split up into timesteps, and the positions and veclocities are updated on a first-order basis like so:

$$\Delta \vec{r}_i=\vec{v}_i\Delta t$$
$$\Delta \vec{v}_i=\sum_{j} \frac{m_j}{\left|\vec{r}_j-\vec{r}_i\right|^3}(\vec{r}_j-\vec{r}_i)\Delta t$$

Notably: This introduces chaos into hypothetically stable systems. Also, the timesteps are not all of equal duration, although I’m not clever enough to know what specific problems that introduces. p5 js doesn’t seem to allow mobile use? i don’t know if that’s actually true or maybe I didn’t do it right; who knows? The site actually totally breaks for mobile users accessing the page so I’ve tried to block it for them.

Anyway here it is!

Also minor update, I got latex working!! So here are Maxwell’s equations:

$$\nabla\cdot\vec{E}=\frac{\rho}{\varepsilon_0}$$
$$\nabla\cdot\vec{B}=0$$
$$\nabla\times\vec{E}=-\frac{\partial\vec{B}}{\partial t}$$
$$\nabla\times\vec{B}=\frac{1}{c^2}\frac{\partial\vec{E}}{\partial t}-\mu_0\vec{J}$$


Tags

Physics · Webdev