- #1
chipotleaway
- 174
- 0
If you rotate your rectangular coordinate system (x,y) so that the rotated x'-axis is parallel to a vector (a,b), in terms of the (x,y) why is it given by
x'=ax+by
y'=bx-ay
I got x'=ay-bx, y'=by+ax from y=(b/a)x.
By the way this is from solving the PDE aux+buy=0 by making one of the partial derivatives disappear. The general solution I got from this change of variables is u(ay-bx) rather than u(bx-ay) - is u(ay-bx) wrong?
x'=ax+by
y'=bx-ay
I got x'=ay-bx, y'=by+ax from y=(b/a)x.
By the way this is from solving the PDE aux+buy=0 by making one of the partial derivatives disappear. The general solution I got from this change of variables is u(ay-bx) rather than u(bx-ay) - is u(ay-bx) wrong?