Explore the fundamentals of Lagrangian mechanics, a reformulation of classical mechanics that simplifies the analysis of complex systems.
Extract
[...] The Chain - Variational Principle 1. If we take a chain element ds whose one end has coordinates and the other y+dy) then this element has a length: So the total length of the chain is: et = 2. In the position where the chain has its minimum potential energy it is immobile and therefore the potential energy of an element of length ds is: And the total potential energy of the chain is: 3. The Lagrange function is therefore: Now to minimize L we use the Beltrami identity: [...]
