Is there an intuitive basis for the Lagrangian?

Mathematech

The additional explanation required by stationary is necessary to get an accurate view of what is going on. You indeed never get a maximum w.r.t. all parameters but a saddle point is not uncommon and with more than one parameter this implies we have a maximum w.r.t to some parameters not a minimum.

Approaches to mechanics that try invoke a non-existant law that nature is magically trying to minimize action ;) just don't work in these very real saddle point cases.

PerpStudent

Thanks for all the comments. It is quite amazing that the Lagrangian is so fruitful in ways that Lagrange could never have imagined. For example, I was just reviewing its application to quantum field theory.
I am continually awed by the mathematical nature of the universe.

didu205

why do nature always take the path of least energy, or in hamilton/lagrange term of least action, im sure this can be answered by quantum mechanics one day and when that day come, i will not be surprise to see physicist controlling energy n matter up to the atoms n quarks.
I became crazy when im learning hamilton and lagrangian mechanics, how difficult problems are magically solved just bey energy considerations.

Jorriss

Quantum mechanics has already answered this. The 'path of least energy' shows up naturally in the path integral formulation.

didu205

Cool, i havent yet started my course modules on quantum mechanics, but im impatient to begin next year in the meantime i watch Susskind on youtube when i can.