zbMATH — the first resource for mathematics

A numerical analysis of chaos in the double pendulum. (English) Zbl 1096.65127
Summary: We analyse the double pendulum system numerically, using a modified mid-point integrator. Poincaré sections and bifurcation diagrams are constructed for certain, characteristic values of energy. The largest Lyapunov characteristic exponents are also calculated. All three methods confirm the passing of the system from the regular low-energy limit into chaos as energy is increased.

65P20 Numerical chaos
70E55 Dynamics of multibody systems
65P30 Numerical bifurcation problems
37M20 Computational methods for bifurcation problems in dynamical systems
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
Full Text: DOI
[1] Ohlhoff, A.; Richter, P.H., Forces in the double pendulum, Z angew math mech, 80, 8, 517-534, (2000) · Zbl 0969.70018
[2] Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; Vetterling, W.T., Numerical recipes in C, (1992), Cambridge University Press Cambridge · Zbl 0778.65003
[3] Wolf, A.; Swift, J.B.; Swinney, H.L.; Vastano, J.A., Determining Lyapunov exponents from a time series, Physica D, 16, 285-315, (1985) · Zbl 0585.58037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.