Some questions about Analytical Mechanics

[Tosh5457]

Hi, I have some questions about some fundamental things of analytical mechanics...

1. The Lagrangian contains all the physical information concerning the system and the forces acting on it. Is that correct? If it is, it only applies to systems where the applied forces are conservative, correct? So isn't that too restrictive?
2. D'Alembert principle only applies to systems where the constraints forces don't do work, right?
3. What are the arguments behind Hamilton's principle? On the book I use (Goldstein) it just comes out of nowhere without any arguments behind it.
4. What is the best book for a formal presentation of Analytical Mechanics? Lagrange and Hamilton were mathematicians, I doubt they presented their work like Goldstein's book presents. The arguments just seem lame to me...

 

[LightHero]

1. Yes, the Lagrangian contains all the physical information concerning the system and the forces acting on it, but it only applies to systems with conservative forces.2. Yes, D'Alembert principle only applies to systems where the constraint forces do not do work. 3. Hamilton's principle states that a dynamical system evolves so as to minimize the action. The principle is based on the notion that the least action (the most efficient path) provides the best description of physical motion. 4. A good book for a formal presentation of Analytical Mechanics is “Analytical Mechanics” by Fowles and Cassiday. It provides a comprehensive introduction to the subject and covers all the topics related to analytical mechanics.