Hamiltonian Mechanics and Hamilton-Jacobi Theory
Hamiltonian mechanics is a transformation theory that is an off-shoot of Lagrangian mechanics. It concerns itself with a systematic search for coordinate transformations which exhibit specific advantages for certain types of problems, notably in celestial and quantum mechanics. As such, the Hamiltonian approach to the analysis of a dynamical system, as it stands, does not represent an overwhelming development over the Lagrangian method. One ends up with practically the same number of equations as the Lagrangian approach. However, the real advantage of this approach lies in the fact that the transformed equations of motion in terms of a new set of position and momentum variables are easily ...
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