Hamiltonian Systems Introduction - Why Study Them?

This course aims to provide students with advanced theoretical and semi-analytical tools for analyzing dynamical systems, particularly mechanical systems. The learning outcomes include understanding Hamiltonian and nonlinear dynamics, writing equations of motion, exploring trajectories in phase space, studying Hamiltonian systems, nonlinear dynamics, periodic orbits, chaos, stability, energy surfaces, and more. The course teaches the comparison between Lagrangian and Hamiltonian formalism, advantages of the Hamiltonian formalism, deriving Hamilton's equations from Lagrange's equations, defining generalized momentum, and exploring Hamilton's canonical equations. The teaching method involves lectures and references to instructor's notes and additional textbooks. The intended audience for this course includes individuals with prior knowledge of Lagrangian systems seeking a deeper understanding of advanced dynamics and nonlinear systems.