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Hamiltonian Formulation
of Mechanics
Descriptions of Motion
in Phase Spaces
The Lagrangian dynamics have been shown to be elegant and straightforward. Half a century after
Lagrange, William R. Hamilton introduced another way of writing the equations of motion of a sys-
tem. Instead of a single differential equation of second order for each coordinate, Hamilton found
a set of twice as many equations but only of the rst order, that is, containing only rst derivatives
with respect to the time. How could Hamilton achieve this?
In the Lagrangian formulation, we can transform to a new set of coordinates as well; ...