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MECHANICS

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Originally appearing in Volume V17, Page 956 of the 1911 Encyclopedia Britannica.
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MECHANICS. The subject of mechanics may be dividedGuided by experience, we are able to frame rules which enable us to say with more or less accuracy what will be the consequences, or what were the antecedents, of a given state of things. These rules are sometimes dignified by the name of " laws of nature," but they have relation to our present state of know-ledge and to the degree of skill with which we have succeeded in giving more or less compact expression to it. They are therefore liable to be modified from time to time, for to be superseded by more convenient or more comprehensive modes of statement. Again, we do not aim at anything so hopeless, or indeed so useless, as a complete description of any phenomenon. Some features are naturally more important or more interesting to us than others; by their relative simplicity and evident constancy they have the first hold on our attention, whilst those which are apparently accidental and vary from one occasion to another are ignored, or postponed for later examination. It follows that for the p•-'rposes of such description as is possible some process of abstraction is inevitable if our statements are to be simple and definite. Thus in studying the flight of a stone through the air we replace the body in imagination by a mathematical point endowed with a mass-coefficient. The size and shape, the complicated spinning motion which it is seen to execute, the internal strains and vibrations which doubtless take place, are all sacrificed in the mental picture in order that attention may be concentrated on those features of the phenomenon which are in the first place most interesting to us. At a later stage in our subject the conception of the ideal rigid body is introduced; this enables us to fill in some details which were previously wanting, but others are still omitted. Again, the conception of a force as concentrated in a mathematical line is as unreal as that of a mass concentrated in a point, but it is a convenient fiction for our purpose, .owing to the simplicity which it lends to our statements. The laws which are to be imposed on these ideal representations are in the first instance largely at our choice. 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. Its success or failure in this respect can only be judged a posteriori. by comparison of the results to which it leads with the facts. It is to be noticed, moreover, that all available tests apply only to the scheme as a whole; owing to the complexity of phenomena we cannot submit any one of its postulates to verification apart from the rest. It is from this point of view that the question of relativity of motion, which is often felt to be a stumbling-block on the very threshold of the subject, is to be judged. By " motion" we mean of necessity motion relative to some frame of reference which is conventionally spoken of as " fixed." In the earlier stages of our subject this may be any rigid, or apparently rigid, structure fixed relatively to the earth. If we meet with phenomena which do not fit easily into this view, we have the alternatives either to modify our assumed laws of motion, or to call to our aid adventitious forces, or to examine whether the discrepancy can be reconciled by the simpler expedient of a new basis of reference. It is hardly necessary to say that the latter procedure has hitherto been found to be adequate. As a first step we adopt a system of rectangular axes whose origin is fixed in the earth, but whose directions are fixed by relation to the stars; in the planetary theory the origin is transferred to the sun, and afterwards to the mass-centre of the solar system; and so on. At each step there is a gain in accuracy and comprehensiveness; and the conviction is cherished that some system of rectangular axes exists with respect to which the Newtonian scheme holds with all imaginable accuracy. A similar account might be given of the conception of time as a measurable quantity, but the remarks which it is necessary to make under this head will find a place later. into two parts: (1) theoretical or abstract mechanics, and (2) applied mechanics. I. THEORETICAL MECHANICS Historically theoretical mechanics began with the study of practical contrivances such as the lever, and the name mechanics Gr. -rd µn7Xavuca), which might more properly be restricted to the theory of mechanisms, and which was indeed used in this narrower sense by Newton, has clung to it, although the subject has long attained a far wider scope. In recent times it has been proposed to adopt the term dynamics (from Gr. 5bpa1.0 force,) as including the whole science of the action of force on bodies, whether at rest or in motion. The subject is usually expounded under the two divisions of statics and kinetics, the former dealing with the conditions of rest or equilibrium and the latter with the phenomena of motion as affected by force. To this latter division the old name of dynamics (in a restricted sense) is still often applied. The mere geometrical description and analysis of various types of motion, apart from the consideration of the forces concerned, belongs to kinematics. This is sometimes discussed as a separate theory, but for our present purposes it is more convenient to introduce kinematical motions as they are required. We follow also the traditional practice of dealing first with statics and then with kinetics. This is, in the main, the historical order of development, and for purposes of exposition it has many advantages. The laws of equilibrium are, it is true, necessarily included as a particular case under those of motion; but there is no real inconvenience in formulating as the basis of statics a few provisional postulates which are afterwards seen to be comprehended in a more general scheme. The whole subject rests ultimately on the Newtonian laws of motion and on some natural extensions of them. As these laws are discussed under a separate heading (MOTION, LAWS OF), it is here only necessary to indicate the standpoint from which the present article is written. It is a purely empirical one. The following synopsis shows the scheme on which the treatment is based Part I. Statics. 1. Statics of a particle. 2. Statics of a system of particles. 3. Plane kinematics of a rigid body. 4. Plane statics. 5. Graphical statics. 6. Theory of frames. 7. Three-dimensional kinematics of a rigid body. 8. Three-dimensional statics. 9. Work. to. Statics of inextensible chains. II. Theory of mass-systems. Part 2.—Kinetics. 12. Rectilinear motion. 13. General motion of a particle. 14. Central forces. Hodograph. 15. Kinetics of a system of discrete particles. 16. Kinetics of a rigid body. Fundamental principles. 17. Two-dimensional problems. 18. Equations of motion in three dimensions. 19. Free motion of a solid. 20. Motion of a solid of revolution. 21. Moving axes of reference. 22. Equations of motion in generalized co-ordinates. 23. Stability of equilibrium. Theory of vibrations.
End of Article: MECHANICS
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