 | Robert Walker - Mechanics - 1830 - 244 pages
...and let 6 be the angle which this trace or the new axis of x' makes with the axis of x, then we have x •=• x/ cos. 6 + y sin. 6, y = — x sin. 6 + y" cos. 6. If we differentiate these values, observing that af, and y are constant for the same element dm, but... | |
 | Robert Walker - Mechanics - 1830 - 268 pages
...and let 6 be the angle which this trace or the new axis of x makes with the axis of x, then we have x = x" cos. 6 + y sin. 6, y = — x sin. 6 + y' cos. 9. If we differentiate these values, observing that x', and y' are constant for the same element dm,... | |
 | Henry Turner Eddy - Curves, Plane - 1874 - 208 pages
...Jj " X y=x sin j. +y cos x . x ' x ' This is the most common transformation, and may also be written x = x' cos 6 — y' sin 6 y = x' sin 6 + y' cos 6, 6 being the angle through which the rectangular axes are revolved. 81. Example. — Refer the point... | |
 | Isaac Todhunter - 1881 - 376 pages
...by changing the direction of the axes. Let the equation be aa2 + bxy + cy2 + dx + ey +/= 0 (1) ; put x = x' cos 6 — y sin 6, y = x' sin 6 + y' cos 6, then (1) becomes x" (a cos2 6 + c sin2 6 + b sin & cos ff) + y" (a sin2 6 + c cos2 6 - b sin 6 cos... | |
 | Edward John Routh - Dynamics, Rigid - 1891 - 436 pages
...axis, and let Gx', Gy1 be the other two principal axes. Let CO = h, Q = angle between Cx' and Ox. Then x = x cos 6 + y sin 6\ y = — x sin 6 + y cos 9 \ . z = z — h ) Hence 'Zmx'z' = cos S^mxz + sin 62myz} _ - . . — h (cos 6^,mx + sin Y = — sin... | |
 | Frederick Harold Bailey - Geometry, Analytic - 1897 - 392 pages
...we rotate the axes about OZ as an axis through any angle 6, the formulas of transformation will be x = x' cos 6 — y' sin 6, y = x' sin 6 + y' cos 6, z = z'; for in [8], § 9, oi = tf, ft = 90°-0, yi =90°, a 2 = 90° + 6, /3, = 6, y 2 = 90°, a 8... | |
 | Frederick Harold Bailey - Geometry, Analytic - 1902 - 392 pages
...that x0, y0, and 6 are all positive. The formulas of transformation to the new axes are by [20], §44, x' = x" cos 6 — y" sin 6, y' = x" sin 6 + y" cos 0. Substituting in (5), we have THE GENERAL EQUATION. F,o. 106. We must now determine 6 so that the... | |
 | Forest Ray Moulton - Celestial mechanics - 1902 - 412 pages
...form as before. (2) Rotate the x and y-axes around the z-axis through the angle 6. The substitution is \x = x cos 6 —y sin 6, \ y = x sin 6 + y cos 6. The first two equations of (34) become x cos 0 - y' sin 0 = cos 0 ' ' ,, sin 0 x sin 0 + y cos 0 =... | |
 | Forest Ray Moulton - Celestial mechanics - 1902 - 414 pages
...CENTER OF GRAVITY (2) Rotate the x and y-axes around the z-axis through the angle 6. The substitution is (x = x cos 6 — y' sin 6, \ y = x' sin 6 + y cos 6. The first two equations of (34) become nn 2 mixi x cos 6 — y sin 0 = cos 0 , sin 6 i^2 '~' x sin... | |
 | Leander Miller Hoskins - Mechanics - 1903 - 484 pages
...coordinates of any point referred to OX and OY, and x', y ' its coordinates referred to OX' and O Y', x' — x cos 6 -\- y sin 6, y' — — x sin 6 + y cos 6 ; x'y' — — x' sin 6 cos 6 + .rKcos' 6 — sin' 6) + y' sin 6 cos 6 = xy cos 26 -f- |(y — .r')... | |
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The coordinates of the vector in the ox'y' system are (x',y') and, furthermore, as may be verified, x' = x cos 6 + y sin 6 y 
