• Flipnik – Intermediate Axis Theorem (Dzhanibekov Effect) Physics T-Shirt – white
  • Flipnik – Intermediate Axis Theorem (Dzhanibekov Effect) Physics T-Shirt – male model, black
  • Flipnik – Intermediate Axis Theorem (Dzhanibekov Effect) Physics T-Shirt – flat lay, black
1 3

FlipnikIntermediate Axis Theorem (Dzhanibekov Effect)

Flipnik – Intermediate Axis Theorem (Dzhanibekov Effect) Physics T-Shirt

$29.99 USD
$29.99 USD
Sale Sold out
Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Color
White · Black
Size
S–5XL
Made
To order · shipping times

Why does a spinning wing nut keep flipping in space? Any rigid body has three principal axes. Spin about the axis with the largest or smallest moment of inertia is stable, but spin about the intermediate one is not, so it periodically flips. Cosmonaut Vladimir Dzhanibekov famously filmed it in orbit, and Flipnik keeps that flip. Pixel-art unisex tee; equation, symbols and sources in the physics panel below.

Color
Size

Size guideS–5XL · inches

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

ShippingFree US

Free US shipping · $10 flat shipping outside the US. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Spin a T-handle, a book or a tennis racket about its longest or its shortest axis and it spins steadily. Spin it about the middle axis and it flips over, again and again.

Euler's equations for a rigid body show why: a small wobble about the intermediate axis grows exponentially, while wobbles about the other two just oscillate. Cosmonaut Vladimir Dzhanibekov filmed a wing nut doing it in orbit in 1985.

Strictly, the other two axes are stable only without energy loss. Flipnik's T-handles flip. The middle axis betrays.

Equations

\[I_1\dot\omega_1 = (I_2 - I_3)\,\omega_2\,\omega_3\quad\text{(and cyclic)}\]
\[\ddot{\delta} = \frac{(I_2 - I_1)(I_3 - I_2)}{I_1 I_3}\,\omega_2^{2}\,\delta,\qquad I_1 < I_2 < I_3\]
SymbolMeaningUnit
\(I_1, I_2, I_3\) principal moments of inertia, smallest to largest \(\mathrm{kg m^2}\)
\(\omega_1, \omega_2, \omega_3\) angular velocity components along the principal axes \(\mathrm{rad/s}\)
\(\delta\) small wobble away from spin about the intermediate axis \(\mathrm{rad/s}\)

Sources

  1. Ashbaugh, Chicone & Cushman (1991) The twisting tennis racket, J. Dyn. Differ. Equ. 3, 67
  2. Landau & Lifshitz, Mechanics (3rd ed., 1976) §37 Euler's equations (citation only)
View full details

Field notes

View all
1 3
View all