A treatise on gyrostatics and rotational motion . y well. The path of an axial point is shown in stereographic projection from theLowesl point of the sphere, and the successive points marked 0, 1, 2, 3, ..., 9, which startfrom the contact with the lower circle, show the positions after successive intervals oftime, each equal to J of the half period of 026 second. The rest of the path for any timewhatever is given by proper repetitions of the portion here shown. XII (WLCTLATION OF PATH OF AXIS OF A Top 263 The reader will have no difficulty in making oul these repetitions. The path, after the p
A treatise on gyrostatics and rotational motion . y well. The path of an axial point is shown in stereographic projection from theLowesl point of the sphere, and the successive points marked 0, 1, 2, 3, ..., 9, which startfrom the contact with the lower circle, show the positions after successive intervals oftime, each equal to J of the half period of 026 second. The rest of the path for any timewhatever is given by proper repetitions of the portion here shown. XII (WLCTLATION OF PATH OF AXIS OF A Top 263 The reader will have no difficulty in making oul these repetitions. The path, after the part numbered I, _ 9 has been described, passes on to touch the outer circle a little below the extreme left, then passes inward again, touches the inner circle on the right t the highest point 0 f the diagram, then passes down to touch tl nter circle near the lowest point. Thence it passes upward and inwards to touch the inner circle abovethe centr i the left, thence to touch the outer circle above the extreme right, and so on. 0. Fig. 65. The formulae given in 19 for the calculation of the azimuthal motion show the effectsof varying the spin and the sidelong motion at the upper limiting circle, in altering theamount of swinging round of the path. The effect, for example, of continual increase ofspin from a small value to a large, with the sidelong motion at the upper circle kept zero,will be to give at first extreme cases of Fig. 22, p. 97, with the cusped indentationswide, then smaller and smaller cusped elements, until a regular sequence of microscopicelements is obtained, which simulates but is not really steady motion. It is Klein andSommerfelds pseudo-regular precession. The reader may notice that to the path forinfinitely rapid spin no tangent can lie drawn except the lower circle, which touches allthe undulations. It is impossible to illustrate the different cases here. A conspectus of diagrams will begiven at the end of the book, with descriptive notes on the different
Size: 1579px × 1583px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, bookidtreatiseongyrost00grayric
