Ying-Jing Qian

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.

On the Perturbation Methods for Vibration Analysis of Linear Time-Varying Systems

Some perturbation methods in the studying vibrations of the linear time-varying (LTV) system are discussed. Three classical perturbation methods, namely, averaging method, harmonic balance method, and multiple scales method with linear scales, have been used from a new perspective based on analytical approximations to the corresponding LTV ordinary differential equations. The deploying beam model has been taken as an example to validate the explicit approximate solutions obtained by these perturbation methods. It is demonstrated that such approximate solutions have good agreement with numerical and exact solutions, excluding the vicinity of the turning point.

Free Vibration Analysis of Pipes Conveying Fluid Based on Linear and Nonlinear Complex Modes Approach

In this paper, linear and nonlinear complex modes are used to analyze the free vibration of pipes conveying fluid involving the gyroscopic properties of the system. The natural frequencies, complex...

Planar periodic orbits’ construction around libration points with invariant manifold technique

This paper revisits the planar periodic motions around libration points in circular restricted three-body problem based on invariant manifold technique. The invariant manifold technique is applied to construct the nonlinear polynomial relations between ξ-direction and η-direction of a small celestial body during its periodic motion. Such direct nonlinear relations reduce the dimension of the dynamical system and facilitate convenient approximate analytical solutions. The nonlinear directional relations also provide terminal constraints for computing periodic motions. The method to construst periodic orbits proposed in this study presents a new point of view to explore the orbital dynamics. As an application in numerical simulations, nonlinear relations are adopted as topological terminal constraints to construct the periodic orbits with differential correction procedure. Numerical examples verify the validity of the proposed method for both collinear and triangular libration cases.

Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series

The restricted three-body problem (R3BP) and restricted four-body problem (R4BP) are modeled based on the rotating frame. The conservative autonomous system for the R3BP and nonautonomous system with period parametric resonance due to the fourth body are derived. From the vibrational point of view, the methodology of polynomial series is proposed to solve for these problems analytically. By introducing the polynomial series relations among the three directions of motion, the three-degree-of-freedom coupled equations are transferred into one degree-of-freedom containing the full dynamics of the original autonomous system for the R3BP. As for the R4BP case, the methodology of polynomial series combined with the iterative approach is proposed. During the iterative approach, the nonautonomous system can be treated as pseudoautonomous equation and the final polynomial series relations and one-degree-of-freedom system can be derived iteratively.

Homotopy Analysis Method for Multi-Degree-of-Freedom Nonlinear Dynamical Systems

In reality, the behavior and nature of nonlinear dynamical systems are ubiquitous in many practical engineering problems. The mathematical models of such problems are often governed by a set of coupled second-order differential equations to form multi-degree-of-freedom (MDOF) nonlinear dynamical systems. It is extremely difficult to find the exact and analytical solutions in general. In this paper, the homotopy analysis method is presented to derive the analytical approximation solutions for MDOF dynamical systems. Four illustrative examples are used to show the validity and accuracy of the homotopy analysis and modified homotopy analysis methods in solving MDOF dynamical systems. Comparisons are conducted between the analytical approximation and exact solutions. The results demonstrate that the HAM is an effective and robust technique for linear and nonlinear MDOF dynamical systems. The proof of convergence theorems for the present method is elucidated as well.Copyright