M. Fabbrichesi , SISSA

In this lesson the professor start the derivation of the Lagrangian formulation from Newton’s equations, for this purpose he first introduce the **generalized coordinates** and velocities, then he introduce the **Holonomic** and Non-Holonomic constraints and finally he derive the **D'Alembert's principle**. Using all of this he derive the first part of the Lagrangian leaving the second part for the next lesson.

Holonomics Constraints and Generalized Coordinates (complementary material)

PAUSE THE VIDEO IF YOU NEED MORE TIME TO TAKE NOTES.

This is the first video in the Analytical Mechanics series. This series starts out with Lagrangian mechanics starting with constraints(this video). Holonomics constrains.

D' Alembert's Principal and Lagrange's Equations of Motion (complementary material)On the second slide, **there is a typo**. A constraint force is a force applied by the holonomic constraint to keep the system of particles consistent with the constraint. Also, the expression for Total Kinetic Energy must have a summation sign(over the "i" indicies).