Manuscript Oai212-A@1 · Oai212-A.tex · section · 79323841

Radial speed, normal speed, and promoted cones

The macroscopic transfer theorem and geometric corrections › Radial speed, normal speed, and promoted cones · lines 468–484

For a Euclidean unit vector $u$ , the radial macroscopic speed is

v_{rad} (u) = \frac{1}{μ ( u )} .

It is continuous because every norm is continuous and positive away from zero. This continuity does not require 212-02.

The supporting-line velocity in unit normal direction $n$ is instead

v_{normal} (n) = h_{B} (n) = μ (x) \leq 1 sup n \cdot x .

These generally differ. Neither is, without additional physical structure, an observer-invariant speed.

Displayed formulas in this passage

unlabeled · line 471
$v_{rad} (u) = \frac{1}{μ ( u )} .$
unlabeled · line 478
$v_{normal} (n) = h_{B} (n) = μ (x) \leq 1 sup n \cdot x .$