ON THE FUNDAMENTL FORMULÆ OF DYNAMICS
15
If the variations , etc. are capable both of positive and of negative values, we must have
etc.,
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(29)
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oretc.
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(29)
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To illustrate the use of these equations in a case in which , etc. are not exact differentials, we may apply them to the problem of the rotation of a rigid body of which one point is fixed. If denote infinitesimal rotations about the principal axes which pass through the fixed point, , will denote the moments of the impressed forces about these axes, and the value of will be given by the formula
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where , and are constants, being the moments of inertia about the three axes. Hence,
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and the equations of motion are
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