Improving implementations for Verlet Integration

[Butt4cak3]

1. Printing inside the individual functions vs. printing in main

Some of the code examples print the results directly inside the verlet function. Others have the functions return the results and print them in main.

With #243, we're already steering in the direction of printing in main instead of the individual functions. To keep everything in line, we should do this in every example.

2. Using the velocity variable in Stormer-Verlet

Currently, the chapter about Verlet Integration includes code examples for the Stormer-Verlet and Velocity-Verlet methods. Both of them have a velocity term, but it's completely unused in Stormer-Verlet. The variable is assigned a value which is never actually used. In #256, @leios and I already agreed that it would be an improvement to also print the velocity. I want to leave this up for discussion before we decide on it.

I think that if we print the velocity for Stormer-Verlet, we should also print it for Velocity-Verlet.

Progress

If we were to change these 2 things, these are the languages examples that would need adjustment:

• C (Update C implementations for Verlet algorithms #298)
• C++ (both)
• Java (Implementation Edit to Verlet Integration in Java #290)
• JavaScript (print velocity)
• Julia (both)
• Python (Reimplemented Verlet Integration in Python #256)
• Rust (Update Rust implementations for Verlet algorithms #297)

Feel free to post your opinion on the second topic and to submit PRs for the listed languages. I will keep this list updated as the code comes in.

[berquist]

For point 2, it should be more clear which form of the velocity equation is being calculated, the one at t or the one at t + dt.

[Butt4cak3]

I don't know what you mean. Nothing about that changes. All we do is take the value that's already there and print it instead of ignoring it.

[berquist]

According to both the book and Wikipedia, there is the form where the velocity is calculated one step behind (t) with error squared in t, and the form where velocity is calculated at the same step (t + dt) with error linear in t. Because there are multiple choices for defining the velocity, it should be stated which one is used in the code. I suppose it's clear from "Here's what it looks like in code", but the divergence in how this is presented in the two articles was temporarily confusing.