P2_14 - at left Final location 20°S 30°W(b This rotation...

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UNIVERSITY OF CALIFORNIA College of Engineering Professor R. Gronsky MSE 104 Solution 2-14 Problem 2-14 Pole A, whose coordinates are 20°N, 50°E, is to be rotated about the axes described below. In each case, find the coordinates of the final position of pole A and show the path traced out during its rotation. a) 100° rotation about the NS axis, counterclockwise looking from N to S . b) 60° rotation about an axis normal to the plane of projection, clockwise to the observer. c) 60° rotation about an inclined axis B, whose coordinates are 10° S , 30° W , clockwise to the observer. Solution (a) This rotation of 100° causes pole A to rotate into the lower hemisphere of the projection sphere after 40°, so its “negative” pole reappears to complete the remaining 60°, as shown below
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Unformatted text preview: at left. Final location: 20°S, 30°W. (b) This rotation of 60° is simply done by spinning about a pin through the center, shown below at right. Final location: 27°S, 48°E. Solution 2-14 2 (c) Rotation about an inclined axis requires that the rotation axis be placed in a useful orientation. That makes this solution a three-step procedure. First, rotate the rotation axis 30°E and 10°N to position it on the center of the stereographic projection, which makes the rotation axis normal to the page. This same operation must be applied to Pole A, locating it at 30°N, 80°E. Second, rotate the full projection by spinning it the required 60° about a pin in the center. Finally, restore the original orientation by a reverse 10°S and 30°W rotation. Final location: 39°S, 51°E....
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  • Spring '08
  • GRONSKY
  • Rigid Body, Rotation, final location, UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science

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P2_14 - at left Final location 20°S 30°W(b This rotation...

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