Maupertuis principle derived from the more general action principle

This video shows how to derive Maupertuis principle from the more general action principle. Then, the path of a particle subject to a potential field is derived by using this principle.

This is an excerpt of the course "Multivariable Calculus and Classical Physics problems".
The first part is on Multivariable Calculus, whereas the second part is about solving advanced mechanics problems. This set of problems is taken from the first volume of the course of theoretical physics by Landau and Lifshitz. I have selected some problems from this book and provided thorough step-by-step solutions in the course; the solutions to these problems are also given in the book but they are usually quite terse, namely not many details are provided. Therefore, what we will do in the course is to first construct the necessary theory to deal with the problems, and then we will solve the problems. Every single formula in this course is motivated/derived.