On a Dynamical Top, for exhibiting the phenomena of
the motion of a system of invariable form about a fixed
point, with some suggestions as to the Earth’s motion
James Clerk Maxwell
[From the
Transactions of the Royal Society of Edinburgh
, Vol. XXI. Part IV.]
(Read 20th April, 1857.)
To those who study the progress of exact science, the common spinningtop is a symbol
of the labours and the perplexities of men who had successfully threaded the mazes of
the planetary motions. The mathematicians of the last age, searching through nature for
problems worthy of their analysis, found in this toy of their youth, ample occupation for
their highest mathematical powers.
No illustration of astronomical precession can be devised more perfect than that presented
by a properly balanced top, but yet the motion of rotation has intricacies far exceeding those
of the theory of precession.
Accordingly, we find Euler and D’Alembert devoting their talent and their patience to
the establishment of the laws of the rotation of solid bodies.
Lagrange has incorporated
his own analysis of the problem with his general treatment of mechanics, and since his time
M. Poinsˆ
ot has brought the subject under the power of a more searching analysis than that of
the calculus, in which ideas take the place of symbols, and intelligible propositions supersede
equations.
In the practical department of the subject, we must notice the rotatory machine of
Bohnenberger, and the nautical top of Troughton. In the first of these instruments we have
the model of the Gyroscope, by which Foucault has been able to render visible the effects of
the earth’s rotation. The beautiful experiments by which Mr J. Elliot has made the ideas of
precession so familiar to us are performed with a top, similar in some respects to Troughton’s,
though not borrowed from his.
The top which I have the honour to spin before the Society, differs from that of Mr
Elliot in having more adjustments, and in being designed to exhibit far more complicated
phenomena.
The arrangement of these adjustments, so as to produce the desired effects, depends on
the mathematical theory of rotation. The method of exhibiting the motion of the axis of
rotation, by means of a coloured disc, is essential to the success of these adjustments. This
optical contrivance for rendering visible the nature of the rapid motion of the top, and the
practical methods of applying the theory of rotation to such an instrument as the one before
us, are the grounds on which I bring my instrument and experiments before the Society as
my own.
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I propose, therefore, in the first place, to give a brief outline of such parts of the theory
of rotation as are necessary for the explanation of the phenomena of the top.
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 Spring '08
 Maxwell
 Angular Momentum, invariable axis

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