# William Hamilton

In existographies, William Rowan Hamilton (1805-1865) (IQ:#|#) (Becker 160:118) (GME:27) [CR:61] was an Irish mathematical physicist, eponym of the Hamiltonian (compare: Lagrangian and Gibbsian), noted for []

Overview
In 1834, Hamilton published the first part of “On a General Method in Dynamics”, which was followed by a second part the following year; the collected works abstract of both is as follows:
[4]

II On a General Method in Dynamics (1834)

This is the first of Hamilton's two famous Essays on dynamics, in which he develops the whole of theoretical dynamics by the aid of one central function. In this Essay he defines his characteristic function by analogy with his researches in optics, and develops its chief properties for a general system of points in any system of coordinates. The remainder of the paper is devoted to methods of approximation with a view to applying them to perturbations of astronomical bodies. At the end he introduces another function, the principal function, which he develops in the Second Essay.

III. Second Essay on a General Method in Dynamics (1835)

Hamilton develops the properties of the principal function in much the same way as in the previous Essay, but he here establishes for the first time his well-known equations of motion. He applies his method to a case of planetary motion, using a system of canonical elements.

In 1865, Clausius, in his "Mathematical Introduction", defined Hamilton's “force-function” as follows: [2]

W = F(x,y,z) + constant

in which the work W done by forces acting on a system of particles can be expressed as a function F(xyz) of rectangular coordinates.

This is one of the founding papers in the science of dynamics, served as a mathematical basis of logic for German physicist Rudolf Clausius’ mathematical foundations, particularly on the calculation of work done or consumed in a system of particles acted on by forces, to his 1865 textbook Mechanical Theory of Heat. [1]

Hamilton was looped into the early thermodynamics network via his correspondence with Scottish mathematical physicist Peter Tait. [3]

Students
In c.1832, Thomas Andrews studied astronomy under Hamilton at Trinity College, Dublin.

Quotes | On
The following are quotes on Hamilton:

“In those cases in which equation (12) holds, or the work done can be simply expressed as a function of the co-ordinates, this function plays a very important part in our calculations. Hamilton gave to it the special name of "force function"; a name applicable also to the more general case where, instead of a single moving point, any number of such points are considered, and where the condition is fulfilled that the work done depends only on the position of the points.”
Rudolf Clausius (1875), The Mechanical Theory of Heat, Second Edition (§: Mathematical Introduction, pgs. 1-20; quote, pg. 11)

Quotes | By
The following are quotes by Hamilton:

“The invention of dynamics as a mathematical science [was founded by] Galileo, and [through] the wonderful extension which was given to that science by Newton—among the successor to those illustrious men: Lagrange has perhaps done more than any other analyst to give extent and harmony to such deductive researches, by showing that the most varied consequences respecting the motions of systems of bodies may be derived from one radical formula; the beauty of the method so suiting the dignity of the results, as to make of his great work a kind of scientific poem.”
William Hamilton (1834), On a General Method in Dynamics

References
1. (a) Hamilton, William R. (1834). “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.” Philos. Trans. R. Soc. London, 124:247-308.
(b) Hamilton, William R. (1835). “A second essay on a general method in dynamics.” Philos. Trans. R. Soc. London, 125:95-144.
2. (a) Clausius, Rudolf. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. (Google Books). London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
(b) Clausius, Rudolf. (1879). The Mechanical Theory of Heat, (2nd ed). London: Macmillan & Co.
3. Wilkins, David R. (2005). Perplexingly Easy: Selected Correspondence Between William Rowan Hamilton and Peter Guthrie Tait (FitzGerald Series). Publisher.
4. Hamilton, William. (1940). The Mathematical Papers of William Rowan Hamilton, Volume Two, Dynamics (editors: A.W. Conway and A.J. McConnell) (abs, pg. xiii) (§1: Problem of Three Bodies by my Characteristic Function, pgs. 1-102; §2: On a General Method in Dynamics, pgs. 103-61; §: Second Essay on a General Method in Dynamics, pgs. 162-211). Cambridge University Press.