Friction or not?

Question

Say I have a differential equation in $mathbb{R}^n$,  Newtons Equation :
begin{align}
    frac{dgamma(t)}{dt}=&dot{gamma}(t),
    nonumber
    
    frac{ddot{gamma}(t)}{dt}=&-nabla V(gamma(t)),
end{align}
where $V:mathbb{R}^dto mathbb{R}$. Does one interpret the $V$ term as a friction term? or an external potential like gravity? I don't know any physics please be kind!

user256872 · Answer

Friction is a non conservative force. A conservative force can be written as the negative gradient of some potential, namely $$vec F_{rm conservative} = -nabla U$$
Since friction is non-conservative, therefore it cannot be described as a gradient of some potential.
Gravity on the other hand is a conservative force. So $V$ can indeed be a gravitational potential.

Friction or not?

One Answer

Add your own answers!

Ask a Question