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Homework Statement
Find the tangential and normal unit vectors for an ellipse with major axis of length a in the x-direction and minor axis of length b in the y-direction.
Homework Equations
For a circle, the unit vectors are defined as
[tex]\hat{r}=\cos{\theta}\hat{i}+\sin{\theta}\hat{j}[/tex]
[tex]\hat{\theta}=-\sin{\theta}\hat{i}+\cos{\theta}\hat{j}[/tex]
The Attempt at a Solution
For the circular case the derivation is easy, one just takes the derivate of
[tex]\vec{r}=r\cos{\theta}\hat{i}+r\sin{\theta}\hat{j}[/tex]
with respect to [tex]\theta[/tex] and r. Now one can take the derivative with respect to [tex]\theta[/tex] and hope that this gives the vector I'm looking for, but I'm not sure. How about the vector normal to the tangent?
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