Lecturer: M. Fabbrichesi , SISSA

In this lesson the professor make an extension of **Hamilton's principle** to non-conservative and non-holonomic systems introducing the method of **Lagrange undetermined multiplier**. He solves three examples using this technique, the problem of a hoop rolling down an inclined plane, one with 4 degree of freedom of a disc that can move in a plane and can rotate around the principal axis and around the center of mass and a more complicated one with 6 degree of freedom, the **two-body problem** with central forces , the motion of the Sun and the Earth.

In this Yale University lesson there are common topics like the problems of gravitational interaction. The three laws of Kepler that are stated and explained. The planetary motion is discussed in general, and how this motion applies to the planets moving around the Sun in particular.