Manuscript XI-A-ST@1 · XI-A-ST.tex · section · c3f0929d

The local transfer rule

The retained host and its three ledgers › The local transfer rule · lines 372–387

XI-A-ST@1#eq:passivedensity

Let $x$ be the developed coordinates and $y$ an orientation-preserving coordinate system on the host laboratory. If $u^{μν}$ is a contravariant rank-two density of weight one, its transported components are

u^{ab} (y) = det \frac{\partial x}{\partial y} \frac{\partial y ^{a}}{\partial x ^{μ}} \frac{\partial y ^{b}}{\partial x ^{ν}} u^{μν} (x (y)) .

Displayed formulas in this passage

XI-A-ST@1#eq:passivedensity · line 378
$u^{ab} (y) = det \frac{\partial x}{\partial y} \frac{\partial y ^{a}}{\partial x ^{μ}} \frac{\partial y ^{b}}{\partial x ^{ν}} u^{μν} (x (y)) .$

Nearby in this section

lemma: Lemma: Supported density transfer
section: The local transfer rule