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Published equation contexts

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

Why this formula appears here

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 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 [ 13 ] . This is an exact…

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MM

Symbol M

M occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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Published contexts (1)

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

Equation 37 · Evolutionary Physics

The Atlas That Refuses to Close

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 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 [ 13 ] . This is an exact…

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