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Equation 37 · Part 4 · The Atlas That Refuses to Close

Symbol v

Δx=S×vMc2,\Delta \mathbf x = \frac{\mathbf S \times \mathbf v}{Mc^2},
vv

What this part means

v occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

v occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

…tensor about the centroid satisfies SαβS^{\alpha\beta}PβP_\beta = 0 — and ask how Xμ(u,Σ)X^\mu(u,\Sigma) moves as u is varied away from the body’s own rest-frame observer to some other inertial observer boosted at velocity v\mathbf v 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 Δx=S×vMc2\Delta \mathbf x = \frac{\mathbf S \times \mathbf v}{Mc^2}. a shift transverse to both the spin and the relative velocity […

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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