Register to reply

What is the physical meaning of curvature?

by cnelson
Tags: curvature, meaning, physical
Share this thread:
cnelson
#1
Oct17-11, 03:16 PM
P: 5
I'm not sure if this belongs here or in the physics section. The mathematical definition of curvature is the derivative of the unit tangent vector normalized to the arc length: [itex]\kappa[/itex] = [itex]\frac{dT}{ds}[/itex]. If we apply this to a parabola with equation y = [itex]x^{2}[/itex] we get [itex]\frac{2}{(1+4x^{2})^{3/2}}[/itex]. This resembles a lorenzian line shape which is the distribution function (amplitude vs frequency) of a harmonic oscillator in a parabolic potential (i.e. a graph of amplitude vs frequency shows a resonance at some frequency.)

My question:

Is the curvature of a potential energy function related to the distribution function of the potential energy function or does it have some other physical relationship that I am missing? Or is the resemblance of the curvature of a parabola and the lorenzian line shape a coincidence?

Sorry if this is kind of vague let me know if you have questions.
Phys.Org News Partner Science news on Phys.org
Suddenly, the sun is eerily quiet: Where did the sunspots go?
'Moral victories' might spare you from losing again
Mammoth and mastodon behavior was less roam, more stay at home
Eynstone
#2
Oct18-11, 09:09 AM
P: 336
The curvature of potential energy is definitely related to distribution function, but the dependence is weird.I can't give any physical meaning to curvature which might suit the dependence.
kdbnlin78
#3
Oct18-11, 10:52 AM
P: 34
The curvature of a surface is (or at least can be) defined as moving a vector through parallel transport around a closed loop.

cnelson
#4
Oct18-11, 12:26 PM
P: 5
What is the physical meaning of curvature?

Thanks for the responses. I'm not familiar with parallel transport so I'll study up and see if it can answer my question.


Register to reply

Related Discussions
The physical meaning of the PDE? Precalculus Mathematics Homework 6
Physical Meaning Quantum Physics 4
Help on physical meaning General Math 6
What is the physical meaning for time? General Physics 6
What is the physical meaning of this eqn Advanced Physics Homework 2