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- Title
Simulation of Delay Effect on Pendulum Oscillations with Limited Excitation.
- Authors
Makaseyev, A. M.; Shvets, A. Yu.
- Abstract
We consider the non-ideal dynamical system "pendulum-electric motor" taking into account the delay effect of the electric motor impulse on the pendulum and delay of the medium reaction on the dynamical pendulum state. The system mathematical model is a system of ordinary differential equations with delay. We propose the approaches reducing the mathematical model of the system to a system of differential equations without delay. We investigate the influence of various factors of delay on steady-state regimes of the system "pendulum-electric motor". The phase-parametric characteristics of the system and dependences of maximum non-zero Lyapunov's characteristic exponent of the delay are constructed and analyzed. The essential influence of the delay on origin, evolution and extinction of the deterministic chaos in the system is shown. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. We ascertain that it is sufficient to use three-dimensional mathematical models for small values of the delay, whereas nine-dimensional mathematical models should be used for relatively high values of the delay.
- Publication
Naukovi visti NTUU - KPI, 2013, Vol 91, Issue 5, p40
- ISSN
1810-0546
- Publication type
Article