Generating Function of a Canonical Transformation - Examples and the Big Picture

This course aims to provide students with advanced theoretical and semi-analytical tools for analyzing dynamical systems, particularly mechanical systems. The course covers topics such as Hamiltonian systems, canonical and non-canonical transformations, nonlinear dynamics, periodic & quasi-periodic orbits, driven nonlinear oscillators, chaos, stability / instability, energy surfaces, and more. Students will learn methods for writing equations of motion and understanding the mathematical structure they represent. The course focuses on sets of possible motion of mechanical systems, trajectories in phase space, and topics related to Hamiltonian systems. The teaching method involves lectures and examples, with a focus on constructing canonical transformations from generating functions. This course is intended for individuals with prior knowledge of Lagrangian systems and an interest in advanced dynamics and nonlinear systems analysis.