Lagranges own proof will be found under DYNAMIcs, Analytical.
He wrote upon nearly every subject of pure mathematics, and also upon theoretical dynamics and spherical and physical astronomy.
In this chapter, I offer forty-three developments, dynamics, and new realities I believe will work together to bring about an end to war.
He applied this principle to the motion of fluids, and gave a specimen of its application at the end of his Dynamics in 1743.
The third volume of the Positive Polity treats of social dynamics, and takes us again over the ground of historic evolution.
But some, especially those on Celestial Dynamics and Organic Motion, are admirable examples of what really valuable work may be effected by a man of high intellectual powers, in spite of imperfect information and defective logic.
During the ensuing two years (1589-1591) he carried on that remarkable series of experiments by which he established the first principles of dynamics and earned the undying hostility of bigoted Aristotelians.
Meanwhile he was filling his note-books as busily as ever with the results of his studies in statics and dynamics, in human anatomy, geometry and the phenomena of light and shade.
His treatment of the subject was the first successful attempt to deal with the dynamics of a system.
Ed., Cambridge, 1896), Dynamics of a Particle (Cambridge, 1898), Rigid Dynamics (6th ed., Cambridge 1905); G.
Of the former, the first, published in 1896, was on the dynamics of a particle; and afterwards there followed a number of concise treatises on thermodynamics, heat, light, properties of matter and dynamics, together with an admirably lucid volume of popular lectures on Recent Advances in Physical Science.
The Dynamics of a Particle was written on the occasion of the contest between Gladstone and Mr Gathorne Hardy (afterwards earl of Cranbrook); and The New Belfry in ridicule of the erection put up at Christ Church for the bells that were removed from the Cathedral tower.
Thomson (Applications of Dynamics to Physics and Chemistry, 47) that on dynamical principles there must be a reciprocal relation between the changes of dimensions produced by magnetization and the changes of magnetization attending mechanical strain.
When generalizing the theory of pendulums of Jacob Bernoulli (1654-1705) he discovered a principle of dynamics so simple and general that it reduced the laws of the motions of bodies to that of their equilibrium.
Dynamics of the movement of the shot up the bore, and of the stress set up in the material of the gun, constitutes the branch of interior ballistics.
In addition to a large number of publications in the Proceedings of the Royal Society and the Philosophical Magazine, he has published A Treatise on the Motion of Vortex Rings (1884); The Application of Dynamics to Physics and Chemistry (1886); Recent Researches in Electricity and Magnetism (1892); Elements of the Mathematical Theory of Electricity and Magnetism (18 95, 5th ed.
Descartes helped to generalize and establish the notion of the fundamental character of uniform motion in a straight line, but otherwise his speculations did not point in the direc tion of sound progress in dynamics; and the next substantial advance that was made in the principles of the subject was due to Huygens (1629-1695).
(The architect being at that time also the contractor.) The chapters are -- (1) on various machines, such as scaling-ladders, windmills, &c.; (2) on windlasses, axles, pulleys and cranes for moving heavy weights, such as those used by Chersiphron in building the great temple of Diana at Ephesus, and on the discovery by a shepherd of a quarry of marble required to build the same temple; (3) on dynamics; (4) on machines for drawing water; (5) on wheels for irrigation worked by a river; (6) on raising water by a revolving spiral tube; (7) on the machine of Ctesibius for raising water to a height; (8) on a very complicated water engine, the description of which is not intelligible, though Vitruvius remarks that he has tried to make the matter clear; (9) on machines with wheels to register the distance travelled, either by land or water; (10) on the construction of scorpiones for hurling stones; (11) and (12) on balistae and catapults; (13) on battering rams and other machines for the attack of a fortress; (14) on shields (testudines) to enable soldiers to fill up the enemy's ditches; (15) on other kinds of testudines; (16) on machines for defence, and examples of their use in ancient times.
In recent times it has been proposed to adopt the term dynamics (from Gr.
The complete determination of the result of a collision under given circumstances is not a matter of abstract dynamics alone, but requires some auxiliary assumption.
The terms affected with the coefficients ~3,-., on the other hand are such as occur in cyclic systems with latent motion (DYNAMICS, Analytical); they are called the gyrostatic terms. If we multiply (33) by 4~.
Whittaker, Analytical Dynamics (Cambridge, 1904); L.
For the later years of his life his labours may be summed up under the following heads: (1) On the conservation of energy; (2) on hydro-dynamics; (3) on electro-dynamics and theories of electricity; (4) on meteorological physics; (5) on optics; and (6) on the abstract principles of dynamics.
This led Clerk Maxwell to frame his theory of electro-dynamics, in which electrical impulses were assumed to be transmitted through the ether by waves.
He made considerable contributions to scientific literature, and among his publications were: An Analytical View of Newton's Principia, with Lord Brougham (1855); an Essay on the Stability of a given State of Motion, which won the Adams' prize in 1877; and treatises on the Dynamics of Rigid Bodies, on Analytical Statics, and on the Dynamics of a Particle.
Another discussed conduction in curved sheets; a third the distribution of electricity in two influencing spheres; a fourth the deter mination of the constant on which depends the intensity of induced currents; while others were devoted to Ohm's law, the motion of electricity in submarine cables, induced magnetism, &c. In other papers, again, various miscellaneous topics were treated - the thermal conductivity of iron, crystalline reflection and refraction, certain propositions in the thermodynamics of solution and vaporization, &c. An important part of his work was contained in his Vorlesungen fiber mathematische Physik (1876), in which the principles of dynamics, as well as various special problems, were treated in a somewhat novel and original manner.
It is understood that the more important contents of the second and third parts appeared in the three voluminous supplements (to the first part) which were published in the same Transactions, and in the two papers " On a General Method in Dynamics," which appeared in the Philosophical Transactions in 1834-1835.
It has the disadvantage of giving the solution of the problem only for a particular case, and of being inapplicable in researches in which the general equations of dynamics have to be applied.
During this period logarithms were invented, trigonometry and algebra developed, analytical geometry invented, dynamics put upon a sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the differential calculus by Newton and Leibnitz and the discovery of gravitation.
For purposes of theoretical discussions relating to moving radiators and reflectors, it is important to remember that the dynamics of all this theory of electrons involves the neglect of terms of the order (v/c) 2, not merely in the value of K but throughout.
Any scheme of abstract dynamics constructed in this way, provided it be self-consistent, is mathematically legitimate; but from the physical point of view we require that it should help us to picture the sequence of phenomena as they aCtually occur.
Balls highly original investigations in kinematics and dynamics were published in collected form under the title Theory of Screws (Cambridge, 1900).
The separation of kinematics from dynamics is due mainly to 0.
APPLIED DYNAMICS; being the theory of machines considered as modifying both motion and force.
Wiseman, Dynamics of Religion (London, 1897), pt.
Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of ellipsoids; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.
The step from optics i to dynamics in the application of the method of " Varying Action " was made in 1827, and communicated to the Royal Society, in whose Philosophical Transactions for 1834 and 1835 there are two papers on the subject.
The interdependence of motion and force was not indeed formulated into definite laws by Galileo, but his writings on dynamics are everywhere suggestive of those laws, and his solutions of dynamical problems involve their recognition.
The term pharmaco-dynamics (4 appaKov, Suvapas, power), which is etymologically more correct, is often used as its equivalent, but it has never become widely adopted.
As this vast mass cooled it must by the laws of heat have contracted towards the centre, and as it contracted it must, according to a law of dynamics, rotate more rapidly.
Thus Bionomics is treated in such articles as Evolution, Heredity, Variation, Mendelism, Reproduction, Sex, &C.; Zoo-dynamics under Medicine, Surgery, Physiology, Anatomy, Embryology, and allied articles; Plasmology under Cytology, Protoplasm, &C.; and Philosophical Zoology under numerous headings, Evolution, Biology, &C. See also Zoological Distribution, Palaeontology, Ocranography, Microtomy, &C.
Webster, Dynamics of Particles, &c. (1904); E.