What is meant by Lagrangian of a dynamical system?

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What is meant by Lagrangian of a dynamical system?
Explain the same for N particle system.
 
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the lagrangian is interpreted as the "action" of a system:

http://en.wikipedia.org/wiki/Action_(physics )
 
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I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
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