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The purpose of this paper is to propose a fuel‐optimal virtual centre selection method for formation flying maintenance in the J2 perturbed environment.

Based on the relative orbital elements (ROE) theory, the J2 perturbed relative motions between different satellites in the formation are analyzed, and then the fuel‐optimal virtual centre selection issue for formation flying maintenance are parameterized in terms of ROE. In order to determine the optimal virtual centre, two theories are proposed in terms of ROE.

Numerical simulations demonstrate that the fuel‐optimal virtual centre selection method is valid, and the control of the ROE of each satellite with respect to a virtual optimal centre of the formation is more efficient regarding the fuel consumption than the control of all satellites with respect to a satellite belonging to the formation.

The fuel‐optimal virtual centre selection method is valid for formation flying mission whose member satellite in circular or near circular orbit.

The fuel‐optimal virtual centre selection approach can be used to solve formation flying maintenance problem which involves multiple satellites in the formation.

The paper proposes a fuel‐optimal virtual centre selection method in terms of ROE, and shows that keeping the formation with respect the optimal virtual centre is more fuel efficient.

The purpose of this paper is to study the effect of J₃ perturbation of the Earth’s oblateness on satellite orbit compared with J₂ perturbation.

Based on the parametric variation method in the time domain, considering more accurate Earth potential function by considering J₃-perturbation effect, the perturbation equations about satellite’s six orbital elements (including semi-major axis, orbit inclination, right ascension of the ascending node, true anomaly, eccentricity and argument of perigee) has been deduced theoretically. The disturbance effects of J₂ and J₃ perturbations on the satellite orbit with different orbit inclinations have been studied numerically.

With the inclination increasing, the maximum of the semi-major axis increases weakly. The difference of inclination disturbed by the J₂ and J₃ perturbation is relative to orbit inclinations. J₃ perturbation has weak effect on the right ascension and argument of perigee. The critical angle of the right ascension and argument of perigee which decides the precession direction is 90° and 63.43°, respectively. The disturbance effects of J₂ and J₃ perturbations on the argument of perigee, right ascension and eccentricity are weakened when the eccentricity increases, simultaneously, the difference of J₂ and J₃ perturbations on argument of perigee, right ascension and argument of perigee decreases with eccentricity increasing, respectively.

In the future, satellites need to orbit the Earth much more precisely for a long period. The J₃ perturbation effect and the weight compared to J₂ perturbation in LEO can provide a theoretical reference for researchers who want to improve the control accuracy of satellite. On the other hand, the theoretical analysis and simulation results can help people to design the satellite orbit to avoid or diminish the disturbance effect of the Earth’s oblateness.

The J₃ perturbation equations of satellite orbit elements are deduced theoretically by using parametric variation method in this paper. Additionally, the comparison studies of J₂ perturbation and J₃ perturbation of the Earth’s oblateness on the satellite orbit with different initial conditions are presented.

The purpose of this paper is to propose a new fuel-balanced formation keeping reference trajectories planning method based on selecting the virtual reference center(VRC) in a fuel-balanced sense in terms of relative eccentricity and inclination vectors (E/I vectors).

By using the geometrical intuitive relative E/I vectors theory, the fuel-balanced VRC selection problem is reformulated as the geometrical problem to find the optimal point to equalize the distances between the VRC and the points determined by the relative E/I vectors of satellites in relative E/I vectors plane, which is solved by nonlinear programming method.

Numerical simulations demonstrate that the new proposed fuel-balanced formation keeping strategy is valid, and the new method achieves better fuel-balanced performance than the traditional method, which keeps formation with respect to geometrical formation center.

The new fuel-balanced formation keeping reference trajectories planning method is valid for formation flying mission whose member satellite is in circular or near circular orbit in J2 perturbed orbit environment.

The new fuel-balanced formation keeping reference trajectories planning method can be used to solve formation flying keeping problem, which involves multiple satellites in the formation.

The fuel-balanced reference trajectories planning problem is reformulated as a geometrical problem, which can provide insightful way to understand the dynamic nature of the fuel-balanced reference trajectories planning issue.

The purpose of this paper is to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.

Based on the concept of fractionated spacecraft, orbit design requirements for cluster flight in the case of fractionated spacecraft are proposed, and categorized into three requirements: stabilization requirement, passive safety requirement, and the maximum inter‐satellite distance requirement. These design requirements are then reformulated in terms of relative eccentricity and inclination vectors (E/I vectors) using a relative motion model based on relative orbital elements (ROEs). By using ROEs theory, the cluster flight orbit design issue is modelled as the distribution of relative E/I vectors for each member satellite in the cluster, and solved by combining three different heuristic search methods and one nonlinear programming (NLP) method.

The simulation results show that the NLP method is valid and efficient in solving the cluster flight orbit design problem and that for some cluster flight scenarios, the heuristic search methods can be adopted to give feasible solutions without the NLP method.

The cluster flight scenario in this paper is limited because the cluster should be in the near‐circular low earth orbit (LEO), and the relative distance between the member satellites should be small enough to satisfy the relative motion linearization assumption.

The cluster flight orbit design method proposed in this paper can be applied by fractionated spacecraft mission designers to propose potential cluster flight orbit solutions.

In this paper, the relative E/I vectors method is adopted to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.

Assembly errors of aeroengine rotor must be controlled to improve the aeroengine efficiency. However, current method cannot truly reflect assembly errors of the rotor in working state owing to difficulties in error analysis. Therefore, the purpose of this study is to establish an optimization method for aeroengine rotor stacking assembly.

The assembly structure of aeroengine rotor is featured. Rotor eccentricity is optimized based on Jacobian–Torsor model. Then, an optimization method for assembly work is proposed. The assembly process of the high-pressure compressor rotor and the high-pressure turbine rotor as the rotor core assembly is mainly considered.

An aeroengine rotor is assembled to verify the method. The results show that the predicted eccentricity differed from the measured eccentricity by 6.1%, with a comprehensive error of 8.1%. Thus, the optimization method has certain significance for rotor assembly error analysis and assembly process optimization.

In view of the error analysis in the stacking assembly of aeroengine rotor, an innovative optimization method is proposed. The method provides a novel approach for the aeroengine rotor assembly optimization and is applicable for the assembly of high-pressure compressor rotor and high-pressure turbine rotor as the rotor core assembly.

The purpose of this paper is to evaluate the safety of formation flying satellites, and propose a method for practical collision monitoring and collision avoidance manoeuvre.

A general formation description method based on relative orbital elements is proposed, and a collision probability calculation model is established. The formula for the minimum relative distance in the crosstrack plane is derived, and the influence of J2 perturbation on formation safety is analyzed. Subsequently, the optimal collision avoidance manoeuvre problem is solved using the framework of linear programming algorithms.

The relative orbital elements are illustrative of formation description and are easy to use for perturbation analysis. The relative initial phase angle between the in‐plane and cross‐track plane motions has considerable effect on the formation safety. Simulations confirm the flexibility and effectiveness of the linear programming‐based collision avoidance manoeuvre method.

The proposed collision probability method can be applied in collision monitoring for the proximity operations of spacecraft. The presented minimum distance calculation formula in the cross‐track plane can be used in safe configuration design. Additionally, the linear programming method is suitable for formation control, in which the initial and terminal states are provided.

The relative orbital elements are used to calculate collision probability and analyze formation safety. The linear programming algorithms are extended for collision avoidance, an approach that is simple, effective, and more suitable for on‐board implementation.

The purpose of this paper is to propose a modified fuel-balanced formation keeping strategy based on actively rotating satellites in the formation in the J2 perturbed environment.

Based on the relative orbital elements theory, the J2 perturbed relative motions between different satellites in the formation are analyzed, and then, the method to estimate fuel required to keep the in-plane and out-of-plane relative motions is presented, based on which a modified fuel-balanced formation keeping strategy is derived by considering both in-plane and out-of-plane J2 perturbations.

Numerical simulations demonstrate that the modified fuel-balanced formation keeping strategy is valid, and the modified fuel-balanced formation keeping strategy requires less total fuel consumption than original Vadali and Alfriend’s method.

The modified fuel-balanced formation keeping strategy is valid for formation flying mission whose member satellite is in circular or near-circular orbit.

The modified fuel-balanced formation keeping strategy can be used to solve formation flying keeping problem, which involves multiple satellites in the formation.

The modified fuel-balanced formation keeping strategy is proposed by considering both in-plane and out-of-plane J2 perturbations, which further reduce the fuel consumption than the original Vadali and Alfriend’s method.

The purpose of this paper is to obtain the reachable domain (RD) for spacecraft with a single normal impulse while considering both time and impulse constraints.

The problem of RD is addressed in an analytical approach by analyzing for either the initial maneuver point or the impulse magnitude being arbitrary. The trajectories are considered lying in the intersection of a plane and an ellipsoid of revolution, whose family can be determined analytically. Moreover, the impulse and time constraints are considered while formulating the problem. The upper bound of impulse magnitude, “high consumption areas” and the change of semi-major axis and eccentricity are discussed.

The equations of RD with a single normal impulse are analytically obtained. The equations of three scenarios are obtained. If normal impulse is too large, the RD cannot be obtained. The change of the semi-major axis and eccentricity with large normal impulse is more obvious. For long-term missions, the change of semi-major axis and eccentricity leaded by multiple normal impulses should be considered.

The RD gives the pre-defined region (all positions accessible) for a spacecraft under a given initial orbit and a normal impulse with certain magnitude.

The RD for spacecraft with normal impulse can be used for non-coplanar orbital transfers, emergency evacuation after failure of rendezvous and docking and collision avoidance.

The purpose of this paper is to verify the feasibility of lunar capture braking through three methods based on particle swarm optimization (PSO) and compare the advantages and disadvantages of the three strategies by analyzing the results of the simulation.

The paper proposes three methods to verify capture braking based on PSO. The constraints of the method are the final lunar orbit eccentricity and the height of the final orbit around the Moon. At the same time, fuel consumption is used as a performance indicator. Then, the PSO algorithm is used to optimize the track of the capture process and simulate the entire capture braking process.

The three proposed braking strategies under the framework of PSO algorithm are very effective for solving the problem of lunar capture braking. The simulation results show that the orbit in the opposite direction of the trajectory has the most serious attenuation at perilune, and it should consume the least amount of fuel in theoretical analysis. The methods based on the fixed thrust direction braking and thrust uniform rotation braking can better ensure the final perilune control accuracy and fuel consumption. As for practice, the fixed thrust direction braking method is better realized among the three strategies.

The process of lunar capture is a complicated process, involving effective coordination between multiple subsystems. In this article, the main focus is on the correctness of the algorithm, and a simplified dynamic model is adopted. At the same time, because the capture time is short, the lunar curvature can be omitted. Furthermore, to better compare the pros and cons of different braking modes, some influence factors and perturbative forces are not considered, such as the Earth’s flatness, light pressure and system noise and errors.

This paper presents three braking strategies that can satisfy all the constraints well and optimize the fuel consumption to make the lunar capture more effective. The results of comparative analysis demonstrate that the three strategies have their own superiority, and the fixed thrust direction braking is beneficial to engineering realization and has certain engineering practicability, which can also provide reference for lunar exploration orbit design.

The proposed capture braking strategies based on PSO enable effective capture of the lunar module. During the lunar exploration, the capture braking phase determines whether the mission will be successful or not, and it is essential to control fuel consumption on the premise of accuracy. The three methods in this paper can be used to provide a study reference for the optimization of lunar capture braking.

The purpose of this research was to analyze application effects of the stable frozen orbit conditions in the spacecraft Orbital Maintenance Maneuver (OMM) reduction.

One challenge in implementing these motions is maintaining the relations as it experiences orbital perturbations (zonal harmonics), most notably due to the non-spherical Earth. A natural phenomenon exists called a frozen orbit, for which the orbital elements: argument of perigee (ω) and eccentricity (e) remain virtually fixed over extended periods of time.

Simulation results show that, using stable frozen orbit condition results in considerable propellant saving, decreased OMM, increase of accuracy position errors and thus performance improvement of the spacecraft for orbiter mission is preferable. So, from among three proposed theories, the Brouwer–Hori theory has provided better accuracy and more stable conditions in the frozen orbit.

Simulation algorithm has been achieved to solve this problem by extracting and combining the equations that govern the frozen conditions with the tangential forces (ΔV) equations for orbit correction.

In all studies with content of harmonic perturbation effects on the spacecraft motion dynamics, main goal is to obtain a solution for optimization of the operation process, so that overshadowed mission costs. The case studies about this aim, mostly to the trajectory parameters optimization by considering the vehicle orbital conditions under various control methods are formed. While in this regards, the intrinsic properties of stable Earth orbits and using them effectively is less than to analyse the problems is considered.