Functions with curvature as parameter


by MrMormon
Tags: curvature, functions, parameter
MrMormon
MrMormon is offline
#1
Dec16-11, 06:03 PM
P: 2
A year ago I learned in multi-var calc about curvature, and since then I've wondered something. It came up again today when my dad tried to talk to me about curvature like it was the second derivative. :P

Is there a way, or at least any attempt or resource at all, about parameterizing a function (2d or 3d) with curvature as the parameter? I've tried but can't derive anything...
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
brydustin
brydustin is offline
#2
Dec17-11, 01:55 PM
P: 209
Quote Quote by MrMormon View Post
A year ago I learned in multi-var calc about curvature, and since then I've wondered something. It came up again today when my dad tried to talk to me about curvature like it was the second derivative. :P

Is there a way, or at least any attempt or resource at all, about parameterizing a function (2d or 3d) with curvature as the parameter? I've tried but can't derive anything...

What you are asking for only kinda makes sense if your function isn't multivariable. Think about it..... Curvature is a function of the variables, as much as the function value is a "function" of the variables; I suppose it might help if you first elaborated what you meant by "parameterizing".
MrMormon
MrMormon is offline
#3
Dec17-11, 09:59 PM
P: 2
Good point. This should be generalizable to any manifold in any number of dimensions, but I'm most specifically thinking about a line in 2D. For example, K(t)=1/t would be a spiral, but is there a way to derive x(t) and y(t) using K(t), because I've never seen this anywhere.

Charles49
Charles49 is offline
#4
Dec19-11, 01:49 PM
P: 87

Functions with curvature as parameter


You might be interested in a related topic called "Prescribed scalar curvature problem." There is a book written on it by J. Kazdan.


Register to reply

Related Discussions
"one parameter family of functions" describing the curve Calculus & Beyond Homework 0
Using the Collocation Method to find a Three-Parameter Solution with Trig Functions Calculus & Beyond Homework 0
Numerical methods to find parameter set with N intersections of 2 implicit functions General Math 0
Gaussian Curvature, Normal Curvature, and the Shape Operator Calculus & Beyond Homework 0
Geodesic Curvature (Curvature of a curve) Differential Geometry 8