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Introduction to Lagrangian
and Hamiltonian Formulations
for Continuous Systems
and Classical Fields
The dynamic systems we have discussed up to this point have their number of degrees of freedom
nite, and they are hence countable. There are some mechanical problems, however, which involve
continuous systems as, for example, the problem of a vibrating elastic solid. Here, each point of the
continuous solid partakes in the oscillations, and the complete motion can only be described by
specifying the position coordinates of all points. The coordinates and momenta of discrete mechan-
ics are replaced by eld quant ...