Elements of Analytical Mechanics
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In our eReader you can find the full English version of the book. Read Elements of Analytical Mechanics Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of Analytical Mechanics
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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.
What to read after Elements of Analytical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Peter Smith Michie to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after Elements of Analytical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Peter Smith Michie to read onlineMoreLess
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