I have an exam in classical mechanics next week, so I came across this problem which I did not fully understand nor any of my colleagues (it was a bonus problem in an old exam) I just want some hint about it, this is the problem:
A particle with mass m is moving without costraint under the effect of the following time and velocity dependent force:
$\vec{F}(\vec{x},\dot{\vec{x}},t)= -2m\vec{\omega(t)}\!\times\!\dot{\vec{x}}-m\vec{\omega(t)}\!\times\!(\vec{\omega(t)}\!\times\!\vec{x}) - m\dot{\vec{\omega}}\!\times\!\vec{x}$
with $\omega(t)$ a time dependent vector.
Show whether we can get this force in the lagrange formalism, from a generalized potential $V(\vec{x},\dot{\vec{x}},t)$
I think that I just have to check if this force curl free is, and I tend to believe that the answer is no because the second and third term won't vanish nor be subtracted from each other (since the first term would directly vanish since it does not depend on the transition).
so My question now whether the way I'm thinking about this problem is valid. I find it a bit confusing what the prefessor means with (in the lagrange formalism). Thank you for your help !
