©2005 Dong Qian All Rights Reserved
1
MECH 321 Notes: Radius of curvature—how it is derived
In the class, I have intentionally skipped (or will, depending on when you
downloaded this notes) the derivation of the relation between the radius of curvature
and the first and second derivatives of a curve. This subject belongs to the topics
covered in differential geometry, which was primary developed by Riemann (Yes
there are two n’s in it). Differential geometry is a great topic. Einstein used it as a
tool to derive his famous theory of relativity (I heard that some of the work was
partially done by his wife at the time, who is a mathematician).
The basic idea in the
differential geometry, if you want me to put it in the simple way, is to realize that
the world (or the space) is not simply flat or straight, and study the properties with
this new philosophy. There are a lot of books on it in the Math library, but I won’t
recommend you to start on it since it needs some preliminary, such as tensor
notation, which will take some time.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '05
 Qian
 Derivative, dt, dt dt, dϕ dϕ, dφ dt dt

Click to edit the document details