Theory Section For Single Pendulum

[brtymn]

Theory Section For Single Pendulum Simulation

The theory section for the single pendulum simulation is needed.

Type of issue

• New Feature
• Bug
• Documentation

Possible Fixes / Implementations

The theory section needs to be written with university level physics.

[Firoda]

What are the things that need to be covered as part of the documentation for a single pendulum. ? If there is a list I can work upon ?

[brtymn]

One of our teammates have written the theory section for the "N-Body Simulation" recently. You can check it out on the website, it is a good example. It will be sufficient to include the fundamentals, nothing too fancy. @Firoda

[20akshay00]

Hey, I worked on creating the simple pendulum simulation on the website. While working on it, these were the main things I had in mind to be written along with it;
Section A:

• Framing the equations of motion of the pendulum, possibly both in cartesian and polar co-ordinates, and emphasizing on why polar might be a better option here.
• The usual small angle approx to get the sinusoidal solution, however with some reference to the actual solution (which involves elliptic integrals that need not be explained, but maybe redirect them to a better source) (I do plan to add the option of comparison of small angle approx pendulum vs. the real pendulum into the simulation sometime soon, so this tidbit in the theory section would complement that.)
• Some introduction on what a phase space is, and how to interpret one (as one of the plots in the sim has the angle vs. angular velocity phase plot.)

Section B:

• A simple introduction for a model of air resistance/dampening forces linearly dependent on velocity. Some reference to observe the phase space plot for the damped pendulum and notice the curve falls inwards, aka, dissipation of net energy of the system.
• In the future, I also plan on adding driving forces, so that opens up the whole discussion on driven oscillations and resonances. So this one isn't needed anytime soon, but its certainly there on the list.

I can help you out with some parts if needed! And if you have your own inputs to add other than this, feel free to do so. It may seem that this includes a lot of things, but it basically covers the full extent of the pendulum model, and perhaps the theory of this can be divided in a way that people don't get too daunted with all the stuff. We still need to figure out the optimal way to convey this content on the website (besides just a long wall of text and equations), so any ideas on that front are appreciated too.

[AeRabelais]

Hi! I'd appreciate being able to contribute to this, if this hadn't already been informally assigned to another person.

[brtymn]

@AeRabelais Great! You can join our Discord server as well so that we can keep in touch. If you are already in the server, just let me know there. I am assigning you!