Celtrix: Rattleback
Mechanics, Chaos & Fluids arc, page 92 of 193. Back to The Pixelated Physics Universe
Who they are
Spin Celtrix the wrong way and she wobbles, rattles, and spins back the other way.
Celtrix is a character of the Mechanics, Chaos & Fluids arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
A rattleback is a boat-shaped top whose mass axes are slightly twisted relative to its curved base (δ ≠ 0). Friction at the contact point couples wobbling to spinning, so in the unfavoured direction spin turns into rocking and then back into spin the other way. Angular momentum is not violated: the friction force at the contact exerts the torque. G. T. Walker analysed it in 1896.
$$ \begin{gathered} \frac{d\mathbf{L}}{dt} = \mathbf{r}_c \times \mathbf{F}_c \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\mathbf{L}$ | angular momentum about the centre of mass | kg·m²/s |
| $t$ | time | s |
| $\mathbf{r}_c$ | vector from the centre of mass to the contact point | m |
| $\mathbf{F}_c$ | contact force from the table (normal force plus friction) | N |
| $\delta$ | skew angle between the principal axes of inertia and the axes of curvature at the contact (δ ≠ 0) | rad |
Honest caveat: Some celts reverse more than once; not every rattleback reverses in only one direction.
Sources
- Garcia & Hubbard (1988) Spin reversal of the rattleback: theory and experiment, Proc. R. Soc. Lond. A 418, 165
- Kondo & Nakanishi (2017) Rattleback: A model of how geometric singularity induces dynamic chirality, Phys. Rev. E 95, 062207
Crossovers
Celtrix meets Whirlda (Euler's Disk). Celtrix and Whirlda are both rigid bodies on a table where friction at the contact point matters. Celtrix's twisted mass axes turn wobble into reversed spin; Whirlda's dissipation makes her wobble speed up until she stops.
Celtrix meets Wobbleon (Chandler Wobble). Celtrix is a top whose spin couples to its wobble. Wobbleon's Earth isn't rigid, and its axis wanders through the crust in the Chandler wobble, with a period of about 433 days rather than the 305 days a rigid Earth would have.
Wear the lore
Concept keywords: Rattleback, Celtrix, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics