What is a dimensional analysis?

Into 3D or possibly 4D? Such as time evolutions?

Yes

But, how do you get around variables influencing homoscedasticity of the curve during time evolutions?

But, how do you get around variables influencing homoscedasticity of the curve during time evolutions? — Shawn

I'd have to know more, and I may not be equipped to give you the best answer, but since you know time is one of you variables, consider describing what it is you are trying to do.

In theory, it's possible afaik. But I may not be the person to consult!

Not plugging.

This may yield you answers as to why it's likely not the tool you use to do analysis on a normal or gaussian distribution, and alternatives suggested.

https://math.stackexchange.com/

The strategy to use it if you insisted on doing so might be to reformulate your problem so that you can decompose a variable into others. But in theory, it's possible, I think!

If it's feasible in any meaningful way would be a question for the guys that hang out at the above url.

It sounds like your problem is general relativity related from an earlier answer.