On stabilizability of the upper equilibrium of the asymmetrically excited inverted pendulum
Using purely elementary methods, necessary and sufficient conditions are given for the existence of T-periodic and 2T-periodic solutions around the upper equilibrium of the mathematical pendulum when the suspension point is vibrating vertically with asymmetric high frequency. The equation of the mot...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2018
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2018.1.45 |
| Online Access: | http://acta.bibl.u-szeged.hu/58140 |
| Tartalmi kivonat: | Using purely elementary methods, necessary and sufficient conditions are given for the existence of T-periodic and 2T-periodic solutions around the upper equilibrium of the mathematical pendulum when the suspension point is vibrating vertically with asymmetric high frequency. The equation of the motion is of the form 1 l (g + a(t)) θ = 0, where a(t) := Ah , if kT ≤ t < kT + Th −Ae , if kT + Th ≤ t < (kT + Th ) + Te (k = 0, 1, . . .); Ah , Ae , Th , Te are positive constants (Th + Te = T); g and l denote the acceleration of gravity and the length of the pendulum, respectively. An extended Oscillation Theorem is given. The exact stability regions for the upper equilibrium are presented. |
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| Terjedelem/Fizikai jellemzők: | 1-19 |
| ISSN: | 1417-3875 |