Ellipses in Mechanics

This lecture covers the geometric locus of points in Cartesian and polar coordinates, focusing on ellipses. It explains the equations in both coordinate systems, the relationship between them, and the parameters (e, p) defining the conic section. The lecture also discusses the central movement in 1/r², applicable to planetary motion, and how to determine the trajectory parameters using the mechanical energy and angular momentum constants. By simplifying equations, the lecture shows how to express the parameters in terms of (a, b) for the conic section. The instructor emphasizes the importance of understanding these concepts to analyze and predict the motion of celestial bodies.