Hamilton, Sir

Hamilton, Sir Wiiiiam Rowan (1805-65) Irish mathematician and physicist. Hamilton invented what is now known as the Hamiltonian formulation of Newtonian mechanics. In doing so, he discovered that there is a very close analogy between Newtonian mechanics and geometrical (ray) optics. He also invented quaternions in mathematics and found a number of applications of quaternions in physics. 

Hamilton (Sir) William Rowan (1805— 1865) Irish mathematician, introducer of quaterions, alternative formalism for tensor and vector calculation, widely used operation by Hamiltonian ... 

One deficiency was lack of inter-service preparation for combined operations. Sir Ian Hamilton, the general in charge at the Dardanelles, was ignorant of the existence of the armoured landing craft that Fisher had ordered for service in the Baltic until told of their existence by naval officers of the Mediterranean fieet. These specialised vessels were not available to him until over three months after the first landings on the Gallipoli peninsula. Most troops went ashore in open boats towed by lighters, and consequently suffered heavy casualties from enemy fire. 

The operator in the brackets in equation (1,14) is known as the Hamiltonian operator, since it is related to an expression for energy given by the Irish mathematician Sir William Rowan Hamilton (1805- 1865) this operator is given the symbol H ... 

Sir William Rowan Hamilton (1805-1865) devised an alternative form of Newton s equations of motion involving a function H, the Hamiltonian function for the system. For a system where the potential energy is a function of the coordinates only, the total energy remains constant with time that is, E is conserved. We shall restrict ourselves to such conservative systems. For conservative systems, the classical-mechanical Hamiltonian function turns out to be simply the total energy expressed in terms of coordinates and conjugate momenta. For Cartesian coordinates x, y, z, the conjugate momenta are the components of linear momentum in the x, y, and z directions p, Py, and p. ... 

The standoff persisted into summer. Sir Ian Hamilton, the Allied commander, Corfu-bom, literary, with a Boer-stiffened right arm and the best of intentions, appealed for reinforcements. The War Cabinet had reorganized itself and expelled Churchill it assented with reluctance to Hamilton s appeal and shipped out fi ve divisions more. 

In simple cases this is the sirni of its kinetic and potential energies. In Hamiltonian equations, the usual equations used in mechanics (based on forces) are replaced by equations expressed in terms of momenta. This method of formulating mechanics (Hamiltonian mechanics) was first introduced by Sir William Rowan Hamilton. 

Two High Couns of Justice were erected by parliament to try, in January 1649, the king (Lilbume was invited, but refused, to be a member), and in February Arthur, Lord Capel (with whom Lilburne was in supportive correspondence), the earl of Hamilton, the earl of Holland, George Lord Goring and Sir John Owen. 

FIGURE 9.3 Sir William Rowan Hamilton (1805-1865). Hamilton reformulated the law of motion of Newton and Lagrange into a form that ultimately provided a mathematical basis for modern quantum mechanics. He also invented matrix algebra. 

Storage, though, is all very well, but how can the information be written and retrieved An exploratory experiment, based, to be sure, on laborious biochemistry, was performed by L. M. Adleman more than a decade ago. As a first demonstration of the watery DNA computer in action he chose to solve a simple form of what mathematicians know as the Hamiltonian path, or travelling salesman problem—how, starting from city A, to travel to each of a succession of other cities, terminating at city Z, without ever retracing your path. A formal solution to this ancient mathematical teaser was worked out in the early nineteenth century by two mathematicians. Sir William Rowan Hamilton in Ireland and Thomas Kirkman in England. With their aid an answer can be easily found if the number of cities is small, but if there are many it requires an enormous amount of computer time. 

Matthews, S. (2004) The Changing Face of Safety , edited version of the 30th Sir Geoffrey de Haviland lecture at the Royal Aeronautical Society, 4 Hamilton Place, London in April 2004 and reported in Aerospace International, October. 

An alternative approach to solving mechanical problems that makes some problems more tractable was first introduced in 1834 by the Scottish mathematician Sir William R. Hamilton. In this approach, the Hamiltonian, H, is obtained from the kinetic energy, T, and the potential ena-gy, V, of the particles in a conservative system. 

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