Normal modes of a double pendulum at low energy levels
This study is concerned with a double pendulum and its regular behaviour associated with low energy levels and the influence of the associated initial conditions on the frequency of normal modes. The case of nonlinear oscillations described by the exact equations of motion is examined. A global qual...
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| Veröffentlicht in: | Nonlinear dynamics 2020-02, Vol.99 (3), p.1893-1908 |
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| container_end_page | 1908 |
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| container_issue | 3 |
| container_start_page | 1893 |
| container_title | Nonlinear dynamics |
| container_volume | 99 |
| creator | Kovacic, Ivana Zukovic, Miodrag Radomirovic, Dragi |
| description | This study is concerned with a double pendulum and its regular behaviour associated with low energy levels and the influence of the associated initial conditions on the frequency of normal modes. The case of nonlinear oscillations described by the exact equations of motion is examined. A global qualitative insight is provided via energy diagrams and Poincaré maps. Then, the case of linear oscillations, their normal modes and associated frequencies is analysed. Further, quantitative insights via two approaches (Lindstedt–Poincaré method and harmonic balancing) are also achieved to determine analytically the influence of initial amplitudes on the existence and frequency of nonlinear normal modes. These results are compared with the one corresponding to the linear normal modes as well as with the corresponding numerical solutions of the exact equations of motion. |
| doi_str_mv | 10.1007/s11071-019-05424-5 |
| format | Article |
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The case of nonlinear oscillations described by the exact equations of motion is examined. A global qualitative insight is provided via energy diagrams and Poincaré maps. Then, the case of linear oscillations, their normal modes and associated frequencies is analysed. Further, quantitative insights via two approaches (Lindstedt–Poincaré method and harmonic balancing) are also achieved to determine analytically the influence of initial amplitudes on the existence and frequency of nonlinear normal modes. 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| ispartof | Nonlinear dynamics, 2020-02, Vol.99 (3), p.1893-1908 |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Automotive Engineering Classical Mechanics Control Dynamical Systems Energy levels Engineering Equations of motion Initial conditions Mechanical Engineering Original Paper Oscillations Pendulums Poincare maps Vibration |
| title | Normal modes of a double pendulum at low energy levels |
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