How can I numerically solve an equation in Unity c#?

Questions & Answers
1

Specifically, I need to solve for x given values of y, a, u and n using this equation:

y = sqrt(a^3 / u) * (x - n * sin(x))

But I haven’t even completed high school and I have no idea where to start. I found something called the Newton-Raphson method that seems to do what I want. Can I translate that method into C#? Is there a more performance-mindful way to do it?

Any help is super appreciated… I’ve been working on this for days and I still have no idea what I’m doing…

Edit: to future googlers, u/Romestus on reddit made this awesome script that solves the equation using Newton’s method. I hope it can help you too!

2

newton-raphson is what i was going to suggest.

i believe for NR you need the derivative of the function as well.
that would be a second function you calculate by hand on paper.
this is a moderately complex function to take the derivative of!

fortunately it looks like it can be simplified a bit.

let’s replace all of sqrt(a^3/u) by a constant k.

so now

y = k * (x - n * sin(x)).

y = (k * x)  - (k * n * sin(x)).

y' = [(k * x)  - (k * n * sin(x))]'.

y' = (k * x)' - (k * n * sin(x))'.

y' = k - k * n * cos(x).

y' = k * (1 - n * cos(x)).

^----- that's your derivative, where k = sqrt(a^3/u).

Then you could either implement NR yourself,
or if you google C# Newton Raphson it looks like there’s a fair number of examples.

3

I would probably look like that:

y = Mathf.Sqrt(Mathf.Pow(a, 3)/u) * (x - n * Mathf.Sin(x))