An elementary treatise on analytic mechanics : With numerous examples (1912)
Bowser, Edward A. (Edward Albert), 1845-1910 · New York : D. Van Nostrand · leaf 340
n, 036e the origin, and OX, OY, anytwo lines through 0 at right anglesto each other, he the axes of co-ordinates. Let (x, y) be theposition of the particle M at thetime t, and (r, 6) its positionreferred to polar co-ordinates,OX being the initial line. Then,calling P the central attractiveforce, we… … x d2y _ dt* w Multiplying the former by y, and the latter by x, andsubtracting, we have d*y _ cPxXdt* y dP Integrating we have = 0. dy dx , xl-yTt=h> where h is an undetermined constant.Since x = r cos 0, and y = r sin 6, we havedx = cos 6 dr — r sin 0 dd,dy = sin 0 dr + r cos 6 dd, which in (3)…
Mechanics, Analytic
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