Equation 34 · The Atlas That Refuses to Close
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Symbol X^mu
u is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol u
varied away from the body’s own rest-frame observer to some other inertial observer boosted at velocity relative to it.
Symbol Sigma
Sigma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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What the article says around this equation
Fix the slicing convention that anchors the centroid to the body’s own rest frame — the choice, standard in the spinning-body literature, in which the spin tensor about the centroid satisfies = 0 — and ask how moves as u is varied away from the body’s own rest-frame observer to some other inertial observer boosted at velocity relative to it. Costa and Natário’s synthesis of the classical spinning-body literature gives the answer in closed form: the centroid measured by the boosted observer is displaced from the rest-frame centroid by
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