What is the Derivation for a Point on a Circle?

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SUMMARY

The discussion centers on the derivation of a point on a circle, specifically addressing the derivative of N with respect to t as presented in Andrew Witkin's slide from a SIGGRAPH course. John initially encountered difficulties in aligning his derivation with the proposed solution but later resolved the issue independently. The key focus is on understanding the relationship between the variables x, r, and t in the context of the bead on wire problem.

PREREQUISITES
  • Understanding of calculus, specifically derivatives
  • Familiarity with parametric equations
  • Knowledge of the bead on wire problem in physics
  • Access to Andrew Witkin's SIGGRAPH course materials
NEXT STEPS
  • Review Andrew Witkin's SIGGRAPH course slides, particularly page 13
  • Study the derivation of parametric equations in calculus
  • Explore the bead on wire problem in more detail
  • Practice deriving derivatives of functions with respect to time
USEFUL FOR

Students and professionals in mathematics, physics, and computer graphics who are interested in understanding the derivation of points on curves and the application of calculus in real-world problems.

ivjohn
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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.
 
Last edited by a moderator:
Physics news on Phys.org
Nevermind. I have solved this problem.
 

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