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# Tag: spinning top

## Forgotten mechanics from the 1800s

**Difficulty level:**★ ★ ★

Are there historical areas of physics we have forgotten about? I have been reading a little of Klein & Sommerfeld’s *The theory of the top* (volume one, 1897). The spinning top might seem just a cute problem. However their work forms a detailed 4-volume set, which took over a decade to complete, and Felix Klein was a leading mathematician. As the translators of a recent English edition (Nagem & Sandri, 2008 ) point out, the book contains one of the earliest occurrences of spinors, applied to the instantaneous position of the top (see #31 of their Translator’s Notes). Also I can’t help but share a quote from Herschel (1851 ), who found a spinning top the best demonstration of the precession of Earth’s rotational axis. This child’s toy:

…becomes an elegant philosophical instrument, and exhibits, in the most beautiful manner, the whole phenomenon.

Nagem & Sandri comment, in #57 of their Translator’s Notes:

It was a great surprise for the translators to find that so many prominent nineteenth-century mathematicians devoted their attention to the statics of rigid bodies, and developed it to such an extent. The subject is now neglected entirely in physics and mathematics, and covered only superficially in engineering curricula.

Two sources they mention are Möbius’ *Lehrbuch der statik* (“Statics textbook”, 1837 ) which analyses forces on rigid bodies, and Ball’s *The theory of screws* (1876 ).

You could emphasise that modern physics (relativity and quantum) is *revolutionary*, and of course that is true. But I prefer to emphasise *continuity* with earlier physics. In the present we make constant usage of Lagrangian and Hamiltonian mechanics, even though these are approximately 200 years old. The enduring relevance of Newtonian mechanics should need no introduction. Also I was a little amused to see Archimedes’ principle mentioned in a modern quantum + relativistic context: Unruh & Wald (1982) discuss lowering a box, which contains thermal radiation, on a rope towards a black hole horizon:

The energy delivered to the black hole is minimized when the box is dropped from its “equilibrium point,” i.e., when the tension in the rope is zero. By the Archimedes principle… this occurs when the energy of the box equals the energy of the displaced acceleration radiation.

This buoyancy effect is due to Hawking radiation. This finally resolved a paradox by Bekenstein (1972) , who proposed using a black hole to seemingly convert energy into work with 100% efficiency, which would violate the 2nd law of thermodynamics. For a historical overview, see Israel (1987, §7.10).

So, good work Archimedes! Two millennia and going strong. But which research have we forgotten today?