Coordinate Systems: When to Make the Switch?

[ouchimdead]

We may solve a function or check a theorem but sometimes the mathematics is easier when we switch from different coordinate systems. What can we look for that tells us changing is a good idea?

 

[sophiecentaur]

Hi
The answer to that one is that you need to have done the same thing, successfully, at some earlier stage in a similar problem. It's the sort of thing that teachers are always doing and the poor student always reacts as you have.
It's along the same lines as when they choose the best directions to resolve forces.

I guess the thing to look for would often relate to the symmetry of the situation.

 

[jahaan]

It's a mathematical or physical intuition you have to develop. I would advise you to think about any examples you have encountered (in textbooks or in class), and think about why in that example a coordinate transformation was a good idea. Usually it's because of some spherical or cylindric symmetry.

For example we expect an electric field of a point charge te be equal in magnitude at equal distances from the charge. The coordinate system that works in the same way is the spherical system. There the distance from the origin is simply r, while in a cartesian system it's $$\sqrt{x^2+y^2+z^2}$$

In general you can try to see for each problem what the important magnitudes/functions are. If they are written in simpler form in some coordinate system, use that one.