Optics and Dynamics
Hamilton wrote important contributions to optics and dynamics also.
An early paper on theoretical dynamics called "Caustics" was presented
to Royal Irish Academy 1824. In 1827, Hamilton developed a theory
providing a single function that combines
mechanics, optics and mathematics. Actually it helped in creating the wave
theory of light itself leading to his "Systems of Rays" which was
printed in 1828 in the Transactions of the Royal Irish Academy.
The principle of "Varying Action" is the great achievement of these works.
The step from optics to dynamics in the application of this method
was made in 1827. "On a General Method in Dynamics" appeared 1834 and 1835.
One of the greatest values of his works was the fundaments he layed, which
were extended with works of Sir Isaac Newton and Joseph Louis Lagrange. C. G. J.
Jacobi and other mathematicians who extended Hamiltonís processes,
leading to additions to our knowledge of differential equations.