Timeline for Why are integrals over cycles called periods?
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| May 21, 2010 at 17:09 | comment | added | José Figueroa-O'Farrill | As I said, the pendulum is merely the most easily accessible (to me, at least) example of a mechanical system whose period is given by an elliptic integral. I would agree with you that planetary motion was understood before the pendulum, and taking that as the origin of the term 'period' does not contradict my belief that the term derives from the periodicity of motion. I insist, though, that I cannot back this up with a reference. | |
| May 21, 2010 at 12:42 | comment | added | John Stillwell | Fair enough. I like the pendulum illustration, but I think that there are better bets for the historical origins of the term "period". We know that periodicity was observed in planetary motion before the motion of the pendulum was understood properly, and indeed elliptic integrals arose with the arc length of the ellipse (Wallis 1655) before they arose with the pendulum. | |
| May 21, 2010 at 9:32 | comment | added | José Figueroa-O'Farrill | I simply used the pendulum as an example, to tie this with the elliptic integrals mentioned elsewhere in this thread. My point was that this stems from the notion of periodic motion in mechanical systems. The Kepler problem is one such system and can be treated analogously to the pendulum once conservation of angular momentum is used to arrive at an effective one-dimensional system. Of course, the "modern" way to do Kepler is to exploit the additional symmetry provided by the Laplace-Runge-Lenz vector. The problem then becomes algebraic without the need to integrate. | |
| May 21, 2010 at 2:59 | history | answered | John Stillwell | CC BY-SA 2.5 |