Chapter 3: Problem 3
A particle of unit mass is subject to an inverse-square-law central force $$ \boldsymbol{F}=-\frac{\boldsymbol{r}}{r^{3}} $$ where \(r=|\boldsymbol{r}|\) and \(\boldsymbol{r}\) is the position vector from the origin of an inertial frame. Show that the motion is governed by the Lagrangian $$ L=\frac{1}{2} \dot{r} \cdot \dot{r}+\frac{1}{r} $$ Write down the equations of motion in spherical polar coordinates and show that there are solutions with \(\theta=\pi / 2\) throughout the motion.
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.