Since its early conception, Classical Mechanics has always had close ties with geometry. This connection is not just limited to the shape of trajectories and gives us a lot of insight into the physics of a system. The goal of this semilab is to give campers a glimpse at this relationship. For most of our time, we will focus our attention on the Harmonic Oscillator. Through this example, we will state and solve Hamilton’s equations, discover the link between symmetries and conserved quantities, and discuss the geometry of Poisson brackets.
Pre-requisites: Comfortable with algebraic manipulations, quadratic equations, vectors, and trigonometry. Some familiarity with classical mechanics is strongly preferred but not strictly required.