Buckingham PI implementation with DynamicQuantities

[karthik11135]

This PR contains the implementation of the BuckinghumPI. Necessary tests are also added.

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[ChrisRackauckas]

I assume this is meant to be a part of a larger PR that includes a system transformation?

[karthik11135]

I assume this is meant to be a part of a larger PR that includes a system transformation?

I'm a bit confused. I thought my second PR was supposed to focus solely on Buckingham PI. Could you clarify and guide me on this?

[ChrisRackauckas]

In engineering, applied mathematics, and physics, the Buckingham π theorem is a key theorem in dimensional analysis. It is a formalisation of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters π1, π2, ..., πp constructed from the original variables, where k is the number of physical dimensions involved; it is obtained as the rank of a particular matrix.

https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem

The useful thing her is the " can be rewritten", ie. a transformation of an ODESystem into a new ODESystem that is dimensionless. The buckingham pi is the first step, then the equations being generated to be dimensionless is the second.

[karthik11135]

Sorry for the late response. I was caught up with a bit of college work. I have gone throught the wiki page. I understood that the obtained PI terms are to be substituted in the original equations and that I must ensure there are no dependent variables in the obtained equations. I will work on this.