Register to reply

Dot product of Force and Position as a constant of motion - physical significance?

Share this thread:
sam guns
Mar8-12, 03:12 PM
P: 3
Reason I posted this in the maths help forum is that an equation of this form randomly popped up in a homework I was doing on differential geometry. I started with a one-form ω=dβ (β is a scalar function) and found that if for a random vector v, ω(v) = 0, then

[itex]\frac{d}{dt} \left( \gamma^{i}\frac{\partial\beta}{\partial x^{i}} \right) = 0[/itex]

where γ is the integral curve of v (aka the position if you interpret v as a velocity)

If you interpret the scalar field β as a potential field, then this says that the dot product of position and force is a constant of motion. Understanding it is not really significant to what I am expected to turn in, but regardless, does it have any physical significance?
1. The problem statement, all variables and given/known data
Phys.Org News Partner Science news on
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
Mar8-12, 03:21 PM
Sci Advisor
HW Helper
tiny-tim's Avatar
P: 26,148
hi sam! welcome to pf!

it looks like the formula for a bead sliding along a frictionless rod forced to rotate (irregularly) about a pivot
but, so far as i know, it has no practical significance
sam guns
Mar8-12, 03:33 PM
P: 3
Thanks for your reply! It's kind of what I suspected, for a second I thought it could be some important constant of motion related to the virial theorem or something like that, but I couldn't find anything in my old mechanics textbooks. I guess it's just a curiosity then :)

Register to reply

Related Discussions
Physical significance of vdP (Thermodynamics) Classical Physics 5
Physical significance Introductory Physics Homework 9
What is physical significance of g factor? Quantum Physics 35
Physical significance behind [H, rho]=0 Quantum Physics 5
Physical Significance of Numbers General Physics 4