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Chaos in Robert Hooke’s inverted cone

Médéric Argentina, Pierre Coullet, Marc Monticelli and Germain Rousseaux, Proceedings of the Royal Society of London A, Volume 463, Issue 2081, p. 1259-1269, May 2007

8 mai 2007

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Robert Hooke is perhaps one of the first scientists to have met chaotic motions. Indeed, to invert a cone and let a ball move in it was a mechanical model used by him to mimic the motion of a planet around a centre of force like the Sun. However, as the cone is inclined with respect to the gravity field, the perfect rosace followed by the particle becomes chaotic meanderings. We revisit this classical experiment designed by Hooke with the modern tools of dynamical systems and chaos theory. By a combination of both numerical simulations and experiments, we prove that the scenario of transition to the chaotic behaviour is through a period-doubling instability.

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