On the existence of periodic motions of the excited inverted pendulum by elementary methods
| Autor: | L. Hatvani, L. Csizmadia |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
010102 general mathematics Motion (geometry) 02 engineering and technology 01 natural sciences Suspension (topology) Inverted pendulum 020303 mechanical engineering & transports 0203 mechanical engineering Excited state Pendulum (mathematics) 0101 mathematics Mathematical physics Mathematics |
| Zdroj: | Acta Mathematica Hungarica. 155:298-312 |
| ISSN: | 1588-2632 0236-5294 |
| DOI: | 10.1007/s10474-018-0835-6 |
| Popis: | Using purely elementary methods, necessary and sufficient conditions are given for the existence of 2T-periodic and 4T-periodic solutions around the upper equilibrium of the mathematical pendulum when the suspension point is vibrating with period 2T. The equation of the motion is of the form $$\ddot{\theta}-\frac{1}{l}(g+a(t)) \theta=0,$$ where l, g are constants and $$a(t) := \begin{cases} A &\text{if } 2kT\leq t < (2k+1)T,\\ -A &\text{if } (2k+1)T\leq t < (2k+2)T,\end{cases}\quad (k=0,1,\dots);$$ A, T are positive constants. The exact stability zones for the upper equilibrium are presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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