London: C. J. CLAY AND SONS, CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, AVE MARIA LANE. Glasgow: 263, ARGYLE STREET. Leipzig: F. A. BROCKHAUS. 80773 DYNAMICS OF A PARTICLE WITH NUMEROUS EXAMPLES BY EDWARD JOHN ROUTH, Sc.D., LL.D., M.A., F.R.S., &c., = HON. FELLOW OF PETERHOUSE, CAMBRIDGE ; FELLOW OF THE UNIVERSITY OF LONDON. CAMBRIDGE AT THE UNIVERSITY PRESS 1898 [All rights reserved.] O many questions which necessarily excite our interest and curiosity are discussed in the dynamics of a particle that this subject has always been a favourite one with students. How, for example, is it that by observing the motion of a pendulum we can tell the time of the rotation of the earth, or knowing this, how is it that we can deduce the latitude of the place? Why does our earth travel round the sun in an ellipse and what would be the path if the law of gravitation were different? Would any other law give a closed orbit so that our planet might (if undisturbed) repeat the same path continually? Is there a resisting medium which is slowly but continually bringing our orbit nearer to the sun? What would be the path of a particle in a system of two centres of force? When a comet passes close to a planet does it carry with it in its new orbit some tokens to prove its identity? Such problems as these (which are merely examples) excite our curiosity at the very beginning of the subject. When we study the replies we find new objects of interest. Beginning at the elementary resolutions of the forces we are led on from one generalization to another. We presently arrive at Lagrange's general method, by which when a single function (worthily called after his great name) has been found we can write down, in any kind of coordinates, all the equations of motion cleared of unknown reactions. A little further on we find Jacobi's method |