Mathematical introduction and recall: recall of basic concepts in Newtonian mechanics, velocity and acceleration in polar and spherical coordinates, notion of differential equation and some simple differential equations.
Gravity: motion in a central force field (reduction of the two-body problem to a one-body problem), characteristics of the motion and some of their consequences, effective potential energy, formal solution of the problem, analysis of the solution for the case of gravitational force, hyperbolic and elliptical orbits.
Motion of a rigid body: vector character of angular velocity and angular momentum, gyroscope, moment of inertia tensor, principal axes, Euler's equations, free rotation and stability.
Non-inertial reference systems: non-inertial systems and inertial forces, uniformly accelerated systems and principle of equivalence, rotating coordinate systems, centrifugal force and Coriolis force, Foucault's pendulum, Brave's pendulum, tides.
