HAMILTON, WILLIAM ROWAN. - THE GENERAL PRINCIPLE OF LEAST ACTION - HAMILTON' S PRINCIPLE.

On a general Method in Dynamics; by which the Study of the Motions of all free Systems of attracting or repelling Points is reduced to the Search and Differentiation of one central Relation, or characteristic Function. Received April 1, - Read April 10, 1834. (+) Second Essay on a general Method in Dynamics. Received October 29, 1834, - Read January 15, 1835. (2 Memoirs).

London, Richard Taylor, 1834-35. 4to. No wrappers as extracted from "Philosophical Transactions" 1834 - Part II. and 1835 - Part I. Both titlepages to the volumes present.Pp. (2),247-308 a. (2),95-144. Both papers clean and fine.

First appearance of these two groundbreaking papers in which Hamilton carries further the dynamics of Lagrange by expressing the kinetic energy in terms of the momenta and the co-ordinates of a system, and discovers how to transform the Lagrangian equations into a set of differential equations of the first order for the determination of of the motion. The Hamilton principle is also called The Principle of "Least Action". The Hamilton Principle as stated in the papers offered here "was the first of his two great "discoveries". he second was the quaternions, which he discovered...1843 nd towhich he devoted most of his efforts during the remaining 22 years of his life."(DSB).

Maupertouis, Euler, and Lagrange introduced the principle of "Least Action" covering the science of dynamics, and now Hamilton brought the principle into a form which was capable of expressing all the laws of Newtonian science in a representation as minimum-problems, that is, all gravitational, dynamical and electrical laws could be represented as minimum problems. In 1925 Heisenberg, Born and Jordan showed, that the Hamilton equations are still valid in quantum theory

Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and has even been extended to quantum mechanics, quantum field theory, relativity and criticality theories. Its influence is so profound and far reaching that many scientists regard it as the most powerful single principle in mathematocal physics and place it at the pinnacle of physical science.

Order-nr.: 42329