Lecturer: 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.

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

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).

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