Astrodynamics

Guzzetti, Davide; Howell, Kathleen Connor

2018 Astrodynamics

doi: 10.1007/s42064-017-0012-7

This document reflects the effort of constructing a basis for understanding attitude motion within a multi-body problem with application to spacecraft flight dynamics. The circular restricted three-body problem (CR3BP) is employed as a model for the orbital motion. Then, attitude dynamics is discussed within the CR3BP. Conditions for bounded attitude librations and techniques for the identification of such behavior are presented: initially for a spacecraft fixed at an orbital equilibrium point, and later for a vehicle that moves on non-linear periodic orbit. While previous works focus on specific challenges, this analysis serves to create a more general framework for attitude dynamics within the CR3BP. A larger framework enables additional observations. For example, a linkage is noted between regions of bounded motion that may appear on an attitude grid search map and families of periodic attitude solutions. Finally, coupling effects between attitude and orbit dynamics within the CR3BP, ones that enable new options for trajectory design, are considered an important opportunity, and should be included in a general framework. As a proof of that concept, sailcraft trajectories are generated within a coupled orbit-attitude model only using a sequence of constant commands for the attitude actuators.

Zhang, Chen; Jin, Jin; Kuang , Linling; Yan, Jian

2018 Astrodynamics

doi: 10.1007/s42064-017-0015-4

This paper is based on the second problem of the 8th China Space Trajectory Design Competition (CTOC8). The background is LEO constellation design strategy for monitoring discrete multi-targets with small satellite under J2 model. The difficulty is that the small satellite is equipped with low-cost cameras with limited coverage ability and the targets are distributed separately in a key area, which result in long revisit time or large number of satellites based on traditional design method. In this paper, a specific LEO constellation design method is proposed to cope with the problems. First, grid search and numerical method are performed to construct a database consisting of repeating ground track orbits. Then several orbits are carefully selected by pruning method to visit each target. Finally, repeating ground track constellation is constructed to meet the maximum revisit time constraint. The present method provides a systematic constellation design methodology of remote sensing observation with limited coverage ability, and demonstrates the resulting constellation can obtain rapid revisit frequency over discrete multi-targets with the least number of satellites.

Li, Xiangyu; Qiao, Dong; Barucci, M. A.

2018 Astrodynamics

doi: 10.1007/s42064-017-0016-3

This paper investigates the equilibria and their stabilities in the doubly synchronous binary asteroid systems, which are modelled as the two tri-axial ellipsoids with various shape and system parameters. Particularly, the in uences of shape and system parameters on equilibria are discussed analytically. Firstly, the geometrical models of doubly synchronous binary asteroid systems are established. The dual second degree and order gravity field is employed to approximate the gravitational potential of the system. Six shape and system parameters are defined. Then, based on the linearized perturbation equations, the explicit expressions of the offsets of equilibria in doubly synchronous systems are derived, which clearly illustrate the relationship between the distribution of equilibria and the variations of shape parameters. Further, the approximate expressions are applied to estimate the offsets of equilibria due to parameter errors, respectively. Finally, in order to have a better insight into the equilibriaum structure, the stabilities of equilibria under different system parameters are investigated. In particular, critical regions of triangular equilibria are calculated and the role of the relative distance on the stability is discussed in detail. This study could provide a preliminary analysis of equilibria for the mission design in doubly synchronous binary asteroid systems.

Qian, Ying-Jing; Yang, Lei-Yu; Yang, Xiao-Dong; Zhang, Wei

2018 Astrodynamics

doi: 10.1007/s42064-017-0017-2

Stability for the non-autonomous bicircular four-body model is analytically investigated in this study. The governing equation is derived from Newton's law of gravity. When the distance between the infinitesimal mass and the third primary is expanded as Taylor expansions, the governing equation can be regarded as two parts: the unperturbed conservative system and the small periodically parametric excitations. The unperturbed system's natural frequency and parametric frequency are analyzed for the possibility of principal parametric resonances. The method of multiple scales is applied directly to the governing equation. The stability conditions are obtained analytically for the principal parametric resonance. Numerical method demonstrates the efficiency of the analytical results.

Liao, Chuan; Xu, Ming; Jia, Xianghua; Dong, Yunfeng

2018 Astrodynamics

doi: 10.1007/s42064-017-0018-1

In this paper, the orbit acquisition and maintenance strategies for the repeat-groundtrack orbit are investigated to maintain the ground track of the satellite within a certain range. Two kinds of orbital dynamics models are introduced to calculate the on-orbit state of satellite. One is the orbital propagation model which is of high fidelity and can approximately express the forces acting on the satellite. The other is the design model which is of low fidelity and utilized by the semi-analytical acquisition algorithm to yield the reference repeatgroundtrack orbit. Combining the differential correction and analytical expressions, the results computed by the semi-analytical acquisition algorithm are of relatively high precision compared with the genetic algorithm. At the same time, the computational burden of the semi-analytical acquisition algorithm is far less than the genetic algorithm. Based on the reference orbit, two orbit maintenance strategies which are designed for chemical and electric engines are put forward to correct the orbit in order to make the ground track of satellite shift in a certain range. The application to the Chinese-French Oceanic Satellite mission has well validated the feasibility of these two strategies. Simulation results have shown that the strategy designed for chemical engine can keep the ground track displacement within 200 m, while all the orbit points can possess sub-meter repeat distance through adopting the strategy designed for the electric engine, which satisfies the requirements of the Chinese-French Oceanic Satellite mission.

Zhong, Rui; Xu, Shijie

2018 Astrodynamics

doi: 10.1007/s42064-017-0019-0

This paper studies the thrust regulation of the tethered space-tug in order to stabilize the target towed by a exible tether. To compromise between model accuracy and simplicity, a rigid- exible coupling multi-body model is proposed as the full model of the tethered space-tug. More specifically, the tug and the towed target are assumed as rigid bodies, whereas the exible tether is approximated as a series of hinged rods. The rods are assumed extensible but incompressible. Then the equations of motion of the multi-body system are derived based on the recursive dynamics algorithm. The attitude motion of the towed target is stabilized by regulating the thrust on the tug, whereas the tether-tension-caused perturbation to the tug's attitude motion is eliminated by the control torque on the tug. The regulated thrust is achieved by first designing an optimal control trajectory considering the simplified system model with constraints for both state variables and control input. Then the trajectory is tracked using a neural-network-based terminal sliding-mode controller. The radial basis function neural network is used to estimate the unknown nonlinear difference between the simple model and the full model, while the terminal sliding-mode controller ensures the rapid tracking control of the target's attitude motion. Thrust saturation and tether slackness avoidance are also considered. Finally, numerical simulations prove the effectiveness of the proposed controller using the regulated thrust. Without disturbing orbital motion much, the attitude motion of the tug and the target are well stabilized and the tether slackness is avoided.