Schematic diagram of a symmetrical gyroscope [12, 17].

Contexts in source publication

Context 1

... geometry of the considered problem is illustrated in Figure 1. .e ...

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... results are connrmed by the phase portraits and their time series presented in Figure 10. It follows from these various analyses that the control of the chaotic dynamics of the gyroscope is very eeective when it operates in the opposite direction of the euid velocity under the innuence of the passive control force. ...

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... have a negative impact on the performance of the rotating gyroscope because it would complicate the precise acceleration of Coriolis when the gyroscope will enter this phase. Figure 11 represents the dynamics of the rotating gyroscope when ε � 0 for F between 30 and 50. .us, ...

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... note through this sgure the coexistence of periodic attractors of period 1T, of period 2T, of chaotic attractors, and of attractors of period 2T with chaotic attractors. In the presence of the passive control force (Figure 11), we note when ε � 1 for F between 30 and 50, that the coexistence of attractors of period 2T has disappeared giving way to the coexistence of attractors of period 1T with those of period 2T. Similarly, the coexistence of attractors of period 2T with chaotic attractors is eliminated, leaving room for the coexistence of attractors of period 1T with chaotic attractors. ...

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... can therefore say that the control of the phenomenon of coexistence of attractors is more effective when the control force is applied in the opposite direction of the euid velocity (ε � −1) than in the same direction (ε � 1). Figure 12 shows the eeects of the parameters K and U on the phenomenon of the coexistence of attractors for ε � 1. It is observed that the parameter K does not facilitate the elimination of this phenomenon, whereas for a high value of the velocity U of the euid, the coexistence of attractors of diierent natures as well as chaotic attractors is eliminated. ...

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... enally obtain, in this case, the coexistence of attractors of period 1T. Finally, Figure 13 represents the effects of the parameters K and U on the phenomenon of the coexistence of attractors for ε � −1. In this case, we note that the parameter K of control and the velocity U of the euid eliminate the coexistence of the attractors but preserve the coexistence of the attractors of period 1T. ...

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... this case, we note that the parameter K of control and the velocity U of the euid eliminate the coexistence of the attractors but preserve the coexistence of the attractors of period 1T. Figures 14-16 represent the phase portraits of the system, respectively, for Journal of Control Science and Engineering ε � 0, 1, −1. .ese egures connrm the existence and control of the coexistence of the attractors predicted by Figures 11-13. ...