Regular and chaotic behaviour in an extensible pendulum
- 1 May 1994
- journal article
- Published by IOP Publishing in European Journal of Physics
- Vol. 15 (3), 139-148
- https://doi.org/10.1088/0143-0807/15/3/009
Abstract
The extensible pendulum is studied numerically to illustrate the Hamiltonian transition to chaos. This is an apparently simple system which is well suited to explain concepts related with the onset of chaos. Using Poincare sections we exhibit the low-energy regular motion and the coexistence of stochastic and regular motion at intermediate energies. We employ other diagnostic techniques for checking our conclusions.Keywords
This publication has 13 references indexed in Scilit:
- On the linear theory of the elastic pendulumEuropean Journal of Physics, 1993
- Closed orbits and constants of motion in classical mechanicsEuropean Journal of Physics, 1992
- Deterministic chaos in the elastic pendulum: A simple laboratory for nonlinear dynamicsAmerican Journal of Physics, 1992
- Demonstration of classical chaotic scatteringEuropean Journal of Physics, 1991
- Superintegrability in classical mechanicsPhysical Review A, 1990
- The elastic pendulum: A nonlinear paradigmJournal of Mathematical Physics, 1981
- The swinging spring ? Approximate analyses for low and very high energy, IICelestial Mechanics and Dynamical Astronomy, 1975
- Periodic solutions of a spring-pendulum systemCelestial Mechanics and Dynamical Astronomy, 1973
- The applicability of the third integral of motion: Some numerical experimentsThe Astronomical Journal, 1964
- On the existence of a third integral of motionThe Astronomical Journal, 1963