This text presents a comprehensive overview of classical mechanics, focusing on the principles of minimum action, the Lagrangian and Hamiltonian formulations, and the motion of particles under central forces. It begins with the historical development of the principle of minimum action, starting with Heron of Alexandria and Fermat, and moves on to Newton's laws and the variational calculus. The text then introduces the Lagrangian and Hamiltonian formulations, explaining how they provide a general framework for describing mechanical systems. It discusses the conservation laws, including energy, momentum, and angular momentum, and their derivation from the symmetry properties of physical systems. The text also covers the motion of particles under central forces, including the two-body problem, the equations of motion, and the differential equation of the orbit. It concludes with an example of the dispersion of particles by a central force, illustrating the application of these principles to real-world scenarios. The text is structured into chapters covering various topics in classical mechanics, including the action principle, constraints, phase space, and the Hamiltonian equations of motion. The content is supported by mathematical derivations and examples, providing a thorough foundation in classical mechanics.This text presents a comprehensive overview of classical mechanics, focusing on the principles of minimum action, the Lagrangian and Hamiltonian formulations, and the motion of particles under central forces. It begins with the historical development of the principle of minimum action, starting with Heron of Alexandria and Fermat, and moves on to Newton's laws and the variational calculus. The text then introduces the Lagrangian and Hamiltonian formulations, explaining how they provide a general framework for describing mechanical systems. It discusses the conservation laws, including energy, momentum, and angular momentum, and their derivation from the symmetry properties of physical systems. The text also covers the motion of particles under central forces, including the two-body problem, the equations of motion, and the differential equation of the orbit. It concludes with an example of the dispersion of particles by a central force, illustrating the application of these principles to real-world scenarios. The text is structured into chapters covering various topics in classical mechanics, including the action principle, constraints, phase space, and the Hamiltonian equations of motion. The content is supported by mathematical derivations and examples, providing a thorough foundation in classical mechanics.