Lecture notes on Classical Dynamics

Abstract

This book presents a comprehensive introduction to classical mechanics as it was developed by the end of the 19th century, while also situating it within the broader framework of dynamical systems. Beginning with a general overview of dynamical systems, the text offers a concise review of Newtonian mechanics before advancing to the Lagrangian and Hamiltonian formulations. Core concepts such as Poisson brackets and the Hamilton–Jacobi theory are systematically explored, providing students with a rigorous foundation in analytical mechanics. The book also introduces the canonical perturbation method, preparing the reader to understand more advanced developments in non-linear dynamics. To bridge classical approaches with modern perspectives, an introductory treatment of chaos theory and related non-linear phenomena is provided in the later chapters. Designed for students and learners seeking both a solid grounding in classical mechanics and an accessible pathway to contemporary topics in dynamical systems, the book integrates traditional formulations with insights into modern developments in chaos and non-linear science.