Lagrangian and Hamiltonian Formulations of Mechanics: Calculus of variations, Hamilton's principle of least action, Lagrange's equations of motion, conservation laws, systems with a single degree of freedom, rigid body dynamics, symmetrical top, Hamilton's equations of motion, phase plots, fixed points and their stabilities.
Two-Body Central Force Problem: Equation of motion and first integrals, classification of orbits, Kepler problem, scattering in central force field.
Small Oscillations: Linearization of equations of motion, free vibrations and normal coordinates, forced oscillations.
Special Theory of Relativity: Lorentz transformation, relativistic kinematics and dynamics, E=mc^2.
Hamiltonian Mechanics and Chaos: Canonical transformations, Poisson brackets, Hamilton-Jacobi theory, action-angle variables, perturbation theory, integrable systems, introduction to chaotic dynamics.
References
Classical Mechanics (3rd Edition), Herbert Goldstein, Poole Jr., Charles P., and John L. Safko, Pearson (2001).
Mechanics (3rd edition, Course of Theoretical Physics), L. D. Landau and E. M. Lifshitz, Butterworth-Heinemann (1976).
Introduction to Dynamics, I. C. Percival and D. Richards, Cambridge University Press (1983).
Classical Dynamics: A Contemporary Approach, Eugene J. Saletan and Jorge V. José, Cambridge University Press (1998).
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (4th edition), E. T. Whittaker, Cambridge University Press (1989).
Mechanics: From Newton's Laws to Deterministic Chaos (6th Edition), Florian Scheck, Springer (2018).
Theoretical Mechanics of Particles and Continua, Alexander L. Fetter and John Dirk Walecka, Dover (2003).
Analytical Mechanics, Louis N. Hand and Janet D. Finch, Cambridge University Press (1998).
Examinations