1. Newtonian Mechanics: Axioms. Laws of Dynamics and vector differential equations of motion. Conservation laws.
2. Motion in inertial and non-inertial reference frames:** Fictitious forces and equations of motion. Examples.
3. Coordinate Systems: Expression of the differential equations of motion in Cartesian and curvilinear coordinates. Examples.
4. Dynamics: Equilibrium solutions and stability characterization. Study of conservative systems with 1 degree of freedom using the potential energy method. Phase diagrams.
5. Applications to systems with 1 degree of freedom: harmonic oscillator, simple pendulum, systems with friction, forced oscillations.
6. Central forces: Conservation of angular momentum. Effective potential and study of the equivalent one-degree-of-freedom system.
7. Solution of the equations of motion in fundamental central force fields in Physics: gravitational, Coulomb, and Yukawa forces. The two-body problem.
8. Analytical Mechanics: Constraints and reactions — degrees of freedom. Classification of mechanical systems. Principle of virtual work.
9. D’Alembert’s Principle and Lagrange’s Equations: The Lagrangian function for forces derived from scalar and vector potentials. Examples.
10. Applications: Finding equations of motion and conserved quantities (integrals of motion) using the Lagrangian method.
11. Hamilton’s Analytical Method: The Hamiltonian function, canonical equations, phase space, and integrals of motion. Applications.
12. Hamilton’s Principle and the axiomatic foundation of Mechanics. Physical significance of the principle of least action and its relation to other fields of Physics.