A particle moves in a plane under the influence of a force, acting toward a center of force, whose magnitude is $$F = frac{1}{r^2} left( 1 - frac{dot{r}^2 - 2ddot{r}r}{c^2} ight)$$ where r is the distance of the particle to the center of force. Find the generalized potential which will result in such a force, and from that the Lagrangian for the motion in a plane.
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e., F = -∇V. In spherical coordinates, this becomes F = -dV/dr. Therefore, we can find the potential energy by integrating the force with respect to r: V(r) = - ∫ P dr = - ∫ (1 - r^2) dr = -r + r^3/3 + C, where C is the constant of integration. Show more…
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