0
$\begingroup$

I have an ellipse centered around the origin, defined by the parametric equation: $$(x,y)=(45\cos\theta,15\sin\theta)$$

How can I modify this equation to rotate the ellipse around the top of the semi-minor ($y$) axis?

In the screenshot below, I used $30^\circ$ as an example.
But I need the rotation angle to be an input parameter - in addition to $\theta$.

If the angle should be $330^\circ$ vs. $30^\circ$, that's fine - I'm not sure which direction is which, and I'd just use CAD + trial and error to pick the correct one for my situation anyway.

enter image description here

$\endgroup$

1 Answer 1

1
$\begingroup$

$$ \pmatrix{x'\\ y'-15}= \pmatrix{\cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha} \pmatrix{x\\ y-15} $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.