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The moment of inertia of a body depends on the mass distribution of the body and on the arbitrarily selected axis about which the moment of inertia is defined. The moments of inertia about two of the principal axes are the maximum and minimum moments of inertia of the body about any axis. The third
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287:”, was dismissed because it was significantly greater than the long-accepted 9–10 month period calculated by Euler, Poinsot, et al. and because Chandler was unable convincingly to explain this discrepancy. However, within months, another American astronomer,
399:(no external torques), internal energy can be dissipated during rotation if the body is not perfectly rigid, and any rotating body will continue to change its orientation until it has stabilized around its axis of maximum inertia, where the amount of
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Poinsot’s geometric interpretation of Earth’s polhode motion was still based on the assumption that the Earth was a completely rigid rotating body. It was not until 1891 that the
American astronomer,
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about the Earth’s spin axis. The rigid part of the Earth’s mass is not symmetrically distributed, and this is what causes the
Chandler Wobble, or more precisely, the Earth’s polhode path.
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showing that there was a periodic motion of 14 months in the Earth’s wobble and suggesting that this was the polhode motion. Initially, Chandler’s measurement, now referred to as the “
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when spinning about the intermediate principal axis, and dissipated energy will cause the polhode to start migrating to the object’s axis of maximum
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provided incontrovertible evidence that the Earth rotates. In the fashion of the day, Poinsot coined the terms polhode and its counterpart,
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of the physics of rotating bodies that provided a visual counterpart to Euler’s algebraic equations. Poinsot was a contemporary of
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is dissipated while an object is rotating, this will cause the polhode motion about the axis of maximum inertia (also called the
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the body about that axis. The closer the concentration of mass to the axis, the smaller the torque required to get it spinning
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The concept of polhode motion dates back to the 17th century, and
Corollary 21 to Proposition 66 in Section 11, Book 1, of
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is perpendicular to the other two and has a moment of inertia somewhere between the maximum and minimum.
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of the body as it spins may not be due to external torques, but rather result from energy
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along which the angular velocity passes through the axis of intermediate inertia.
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The details of a spinning body may impose restrictions on the motion of its
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Curve produced by the angular velocity vector on the inertia ellipsoid
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or stabilize, with the polhode path becoming a smaller and smaller
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in torque-free motion. In particular, Euler and his contemporaries
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internally as the body is spinning. Even if angular momentum is
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Rotation about the axis of minimum inertia (also called the
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body inherently has three principal axes through its
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264:(path or way)—thus, polhode is the
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36:verification
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389:orientation
307:Description
301:symmetrical
189:around its
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418:Herpolhode
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393:dissipated
375:separatrix
360:closing in
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231:and whose
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99:April 2019
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468:Mechanics
397:conserved
229:gyroscope
194:spin axis
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58:"Polhode"
407:See also
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183:latitude
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371:inertia
352:ellipse
297:elastic
279:, made
268:of the
147:History
137:polhode
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356:circle
340:energy
311:Every
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262:hodós
251:pólos
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191:polar
187:Earth
90:JSTOR
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270:pole
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257:ὁδός
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