The book Elements of Analytical Mechanics was written by author Peter Smith Michie Here you can read free online of Elements of Analytical Mechanics book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Elements of Analytical Mechanics a good or bad book?
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Comparing this value of Fwith that given in the discussion of motion due to gravity alone (Art. 92), we see that F is the same function of z, but a different function of /. CONSTRAINED MOTION. 155 These results can be more readily obtained by considering- the motion to be free, the body being acted upon by the result- ant of all the forces, including the normal reaction. This re- sultant is Mg sin a — F, and it acts in the direction of the path. 139. Let the circumference OAB (Fig. 52) be in th...e plane xz, and tangent to the axis of x at O. Then we have for the point A, Eq. (372), or — 2 = ^/* sin' a = OA sin a = OB sin* a . . (377) /=/^. (378) which is the time of fall from rest down the diameter of the circle. Hence the time required for the body to pass over any chord of a given circle, the plane of the circle being vertical and the body starting from the upper extremity of the vertical diameter, is independent of its length; that is, the circumference is the locus of simultaneous arrival down all right lines in a vertical plane, these lines having a common point at the origin of motion.
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