What is the Derivation for a Point on a Circle?

[ivjohn]

Hi All,

I am working on the problem of bead on wire and got stuck on some basic derivation detail.
I took the same approach as Andrew Witkin used in his slide (page 13):
http://www.cs.cmu.edu/~baraff/sigcourse/slidesf.pdf

Here is the screenshot of the slide page 13:
http://desmond.imageshack.us/Himg831/scaled.php?server=831&filename=pocs.png&res=medium

As we can see, C is the function of x and r is constant. x is a function of t as well.

I got stuck on deriving the third line of the equation (the derivative of N with respect to t). My derivation result seems different from what the author proposed.
Here is my step by step derivation:
http://img269.imageshack.us/img269/8623/derivative.png

Could somebody point out my mistake? Any help will be greatly appreciated.

Regards,
John.

 

[ivjohn]

Nevermind. I have solved this problem.