Non-linear to linear transformation

[tfleming]

take a point A(x_1,y_1) on a circe centre B (x_2, y_2) and allow the circle to roll along an X-axis; now we all know that the cycloid equation to point A is highly non-linear; so now if we take the point B, we find the problem has been converted into a linear problem;

now do this to E-fields and H-fields between charged points; think about it!

 

[tfleming]

so one point is we see a non-linear problem converted into a linear one via our choice of co-ordinates;

can we apply this knowledge to some of most pressing problems??