Some questions about Analytical Mechanics

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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...
 
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