0
$\begingroup$

I'm trying to solve a problem which includes a spinning object and I want to find it's velocity vector with respect to an object moving in a straight line on the the x axis with constant velocity.

I can represent the spinning object's velocity in cartesian coordinates and subtract from it the velocity of the moving object. But that is a method that doesn't scale if I have a more complex spinning shape. Is there a way to convert the object moving in a straight line to polar coordinates?

What is the x basis vector in polar vector form?

Edit: figured it out. The relation I was looking for was:

$\hat{x}=cos(\theta)\hat{r}-sin(\theta)\hat{\theta}$

Improve this question
$\endgroup$
2
  • $\begingroup$ Are you familiar with the Jacobian matrix? The relation between the basis vectors in polar and Cartesian coordinates is closely related - you can construct it from partial derivatives of one set of variables with respect to the other - but the matrix must have determinant 1 (it's orthogonal). $\endgroup$
    – user138962
    Dec 13, 2018 at 17:45
  • $\begingroup$ It's a lot less sophisticated. I figured it out and edited the post. $\endgroup$
    – Yizhar Amir
    Dec 13, 2018 at 18:11

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.