Saturday, August 17, 2013
Hamilton's Papers on Dynamics
Hamilton's papers on dynamics followed shortly after the one on Paths of Light and the Planets. In them he used the Principal Function to determine the motion of a massive body, pairs of bodies and and also dwelt with the two-body problem with an application to the orbit of a planet about the Sun and the three-body problem. There were two parts.
General Method in Dynamics I (1834)
General Method in Dynamics II (1835)
In the second paper he uses tricks line substituting partials of the Principal Function for a second set of parameters and two sets of first order differential equations giving the time rate of change of the sets of parameters. One can compare the modern versions known as the Hamilton-Jacobi equation and Hamilton's equations.