Minghui Yao

Hidden Attractors and Dynamical Behaviors in an Extended Rikitake System

In this paper, an extended Rikitake system is studied. Several issues, such as Hopf bifurcation, coexistence of stable equilibria and hidden attractor, and dynamics analysis at infinity are investigated either analytically or numerically. Especially, by a simple linear transformation, the wide range of hidden attractors is noticed, and the Lyapunov exponents diagram is given. The obtained results show that the unstable periodic solution generated by Hopf bifurcation leads to the hidden attractor. The existence of hidden attractors that may render the systems behavior unpredictable not only depends on the value of system parameters but also on the value of initial conditions. The phenomena are important and potentially problematic in engineering applications.

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L2 point

Quasi-periodic orbits in the Earth–Moon system are highly sensitive and even small errors in position and/or velocity have strong influence on the trajectory. These types of trajectories are unstable and must be controlled to maintain the corresponding orbits. This paper investigates the stationkeeping strategy for quasi-periodic orbits near the translunar libration point with full consideration of the contribution from the Sun’s gravity and the Moon’s eccentricity, in which the continuous low-thrust is preformed to enforce the probe following several onboard decided target points on the baseline. A new high-fidelity model is derived to describe motions of the quasi-periodic orbits by using the standard ephemerides. Based on the improved multiple-shooting method and the proposed model, a baseline trajectory is obtained. Then, a new continuous low-thrust-based stationkeeping strategy is proposed. Specifically, by employing Gauss pseudospectral method in the stationkeeping algorithm and by introducing the maximal excursion and fixed time interval, the target points on the baseline trajectory are chosen onboard based on real-time data. Simulation results show that the unstable quasi-periodic orbit can be maintained effectively with the low-energy consumption.

The Nonlinear Dynamical Analysis of a Sandwich Plate with In-Plane Loading in Supersonic Flow

Nonlinear dynamics of a sandwich plate with viscoelastic soft core in supersonic flow are investigated by considering the in-plane periodic loading. Using Reddy’s third-order shear deformation theory and von Karman’s nonlinearity, the governing partial differential equations are derived by Hamilton’s principle and then truncated into a set of ordinary differential equations by Galerkin method. The critical speed for flutter is discussed by employing the linear theory. Further, the method of multiple scales is used in the nonlinear dynamical analysis of the truncated system. The Poincare map is numerically calculated to identify dynamical behaviors. The bifurcation diagrams are presented for varying the dimensionless in-plane loading fluctuation amplitude and the Mach number related dimensionless parameter while other parameters are unchanged.