The chapter discusses the principles of classical mechanics, focusing on the "minimum" principles and their historical development. It begins by explaining that the motion of a particle in an inertial system is described by Newton's second law, $\vec{F} = M \vec{a}$, when relativistic effects are negligible. The chapter then introduces the Hamilton principle, which is a general formulation of the law of motion for mechanical systems. This principle characterizes a system by a function, the Lagrangian, and the motion of the system is such that the integral of the Lagrangian over a time interval takes a minimum value. The chapter derives the Euler-Lagrange equations from this principle, which are the equations of motion for the system. The D'Alembert principle is also discussed, which states that the virtual work done by the constraint forces is zero. This principle is used to formulate the equations of motion in terms of the generalized coordinates and momenta. The chapter further explores the concept of phase space, configuration space, and constraints, and introduces Hamilton's equations of motion, which are derived from the Hamiltonian function. The chapter also covers conservation laws, including energy, momentum, and angular momentum, and provides examples of their application. Finally, it discusses the motion under central forces, including the two-body problem, the differential equation of the orbit, Kepler's problem, and the dispersion of particles by a center of force. The example of Rutherford scattering is provided to illustrate the application of these principles in practical scenarios.The chapter discusses the principles of classical mechanics, focusing on the "minimum" principles and their historical development. It begins by explaining that the motion of a particle in an inertial system is described by Newton's second law, $\vec{F} = M \vec{a}$, when relativistic effects are negligible. The chapter then introduces the Hamilton principle, which is a general formulation of the law of motion for mechanical systems. This principle characterizes a system by a function, the Lagrangian, and the motion of the system is such that the integral of the Lagrangian over a time interval takes a minimum value. The chapter derives the Euler-Lagrange equations from this principle, which are the equations of motion for the system. The D'Alembert principle is also discussed, which states that the virtual work done by the constraint forces is zero. This principle is used to formulate the equations of motion in terms of the generalized coordinates and momenta. The chapter further explores the concept of phase space, configuration space, and constraints, and introduces Hamilton's equations of motion, which are derived from the Hamiltonian function. The chapter also covers conservation laws, including energy, momentum, and angular momentum, and provides examples of their application. Finally, it discusses the motion under central forces, including the two-body problem, the differential equation of the orbit, Kepler's problem, and the dispersion of particles by a center of force. The example of Rutherford scattering is provided to illustrate the application of these principles in practical scenarios.