0
$\begingroup$

My first instinct would be to use the force

$$\vec{F} =- \alpha \vec{v}$$

and therefore

$$V(\vec{r}) = \alpha \int_C \vec{v}\cdot d\vec{s} = \alpha \int_C \vec{v}\cdot \vec{v} dt = \alpha \int_C g_{ab} \frac{dx^a}{dt} \frac{dx^b}{dt} dt$$

(where $C$ is the projectile's path) and go from there. Would this work?

$\endgroup$
1
$\begingroup$

Since velocity dependent forces are not conservative, you cannot write them as the gradient of a potential function - ie. you cannot write a potential function as the integral of your non-conservative (dissipative) force. However, you can introduce a dissipative term into the equations and I believe it will work out from there. See, for example, http://www.phys.uri.edu/~gerhard/PHY520/mln9.pdf

or other google links for lagrangian with friction

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.