Mathematical Tracts On the Lunar And Planetary Theories, the Figure of the Earth, Precession And Nutation, the Calculus of Variations, And the Undulatory Theory of Optics. Designed for the Use of Students in the University

Cover Mathematical Tracts On the Lunar And Planetary Theories, the Figure of the Earth, Precession And Nutation, the Calculus of Variations, And the Undulatory Theory of Optics. Designed for the Use of Students in the University
Mathematical Tracts On the Lunar And Planetary Theories, the Figure of the Earth, Precession And Nutation, the Calculus of Variations, And the Undulatory Theory of Optics. Designed for the Use of Students in the University
Sir George Biddell Airy
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And since, by the last Proposition, the angular velocity remains unaltered, angles equal to BAD will be added to BAD in each succeeding interval ; and, therefore, at the end of 1'', the axis of revolution will be inclined to the line, which was the axis of revolution at the beginning of that l", by the 198 PRECESSION AND NUTATION.
angle - . Since the same is true of every successive l", the axis of revolution will move from the position AB, towards the position AC, with the angular velocity - .
...
13. Prop. 5. Under the same circumstances, if a spherical surface be described in the body about the point A, at which the axes intersect each other, the point at which the successive axes of revolution cut this surface, will lie in the circumference of a small circle, whose radius = radius of the sphere x —^ , CO nearly.
Let AB, (fig. 3.), be the original axis, and, as before, suppose l" divided into n parts, and the angular velocity — , about an axis perpendicular to the axis of rotation, to be impressed at the end of each.


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