Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Radius of curvature formula derivation

  1. Sep 4, 2005 #1
    for a curve defined by y=f(x) the radius of curvature is defined as
    [f""(x)/(1+f"(x))] power 3/2. I need a good neat & understandable derivation for that. can any body show a web.
     
  2. jcsd
  3. Sep 4, 2005 #2
    Differential Geometry of Curves

    I don't like the format of the forum reply, so click on the following link to view your derivative: DGC.
     
  4. Sep 4, 2005 #3
    Well first understand that curvature for a vector function is given by:

    [tex]\kappa=\frac{|\mathbf{r}'\times\mathbf{r}''|}{|\mathbf{r}'|^3}[/tex]

    Now, let r = xi + f(x)j and simplify. To prove the first formula [itex]\kappa[/itex], use the following fact and compute r' x r''. The answer should be clear from there.

    [tex]\kappa=\frac{d\mathbf{T}}{ds}[/tex]

    [tex]\mathbf{r}'=\frac{ds}{dt}\mathbf{T}[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?