Part One: Newton΄s three Laws of Motion. Projectile trajectories and other characteristic examples. Force, momentum, kinetic and dynamic energy, work, torque. Conservation principles of momentum, angular momentum, and total mechanical energy. / Oscillations: the harmonic oscillator with damping and external driving force. Non-linear oscillations. The simple pendulum. Phase space. Chaotic dynamics. / Gravity: Newton΄s universal law of attraction. The gravitational field and the gravitational potential. Ocean tides.
Part Two: Elements of the Calculus of Variations, Euler΄s formula, the problem of the brachistochrone and other representative examples. / Hamilton΄s Principle, the Lagrangian, generalized co-ordinates, Euler-Lagrange equations, equivalence with Newton΄s equation of motion. Conservation theorems revisited. The Hamiltonian, Hamilton΄s canonical equations of motion, phase space.
Part Three: Motion in a central force field. The center of mass and the dynamics relative to that. Equivalent one-body problem, reduced mass. Conservation of angular momentum. / Equations of motion and First Integrals. Centrifugal energy and the effective potential. Celestial bodies, Kepler΄s problem and its solution. Planetary orbits and the associated three laws of Kepler.
In order to highlight the special educational and didactical aspects of the course, special emphasis is given to the historical evolution and scientific development of the subject, as well as on its applications in technology and other sciences.