Curvature Referred to Moving Axes

1. Consider a pair of rectangular axes rotating uniformly about the origin.

Let (u, v) be the co-ordinates of a point referred to the moving axes at any time, and let (X,Y) be the co-ordinates of the same point referred to the initial position of the axes, and let 0 be the angle turned through from the initial position.

Then

X=i cosθ -v sin θ.

Y= u sinθ+v cos θ.