Solving Lagrangian Mechanics Homework in 2D Movement

[squareroot]

Homework Statement

So, a particle is moving in a plane under the action of a force F that is oriented at all times to the direction of the center of the force.may r be the distance from the particle to the center of the force generator.

Find the potential generator expression that occurs and the form of the Lagrangian for 2D movement of the particle.

the force F's expression is below

.

Homework Equations

Lagrangian mechanics...

The Attempt at a Solution

okay, so F=-dU/dr so

=

And my question is, how do you solve that integral? the one over r 2dot and r dot?? If anyone could explain that to me it would be great!ty

 

[jack476]

Let me ask you this. If you have r = some function of time, does the function for dr/dt depend on r?