PPT Slide
A Lagrangian, L, for a system is defined as
In one dimension, with conservative forces, you can get
the equations of motion by following the following recipe:
Looks sort of messy, but it is just derivatives
no vectors, no force diagrams, no F=ma stuff
But it is mechanically equivalent!
Euler-Lagrange equations -- you must
keep you partial and total derivatives straight!
It can all be generalized to many dimensions
in different coordinate systems
and with non-conservative forces