Geometric Algebra Applications - Kepler Problem (Part 2)

In this video, we show that the trajectories of masses moving under an inverse-square law are conic sections using geometric algebra. We will not be solving any differential equations, but instead showing that a special vector, the Laplace-Runge-Lenz vector, is a conserved quantity of motion and doing some simple algebraic manipulations to arrive at the equation for a conic section in polar coordinates. References / Further Reading: 1. http://adsabs.harvard.edu/full/1983CeMec..30..151H 2. Lasenby and Doran's "Geometric Algebra for Physicists" 3. https://en.wikipedia.org/wiki/Classical_central-force_problem#Specific_angular_momentum 4. https://en.wikipedia.org/wiki/Specific_relative_angular_momentum 5. https://en.wikipedia.org/wiki/Laplace%E2%80%93Runge%E2%80%93Lenz_vector 6. https://en.wikipedia.org/wiki/Inverse-square_law