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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 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.

Preface The functions of business divide into several areas and the general focus of this book is on one of the most important although least understood of these—DISTRIBUTION. The particular focus is on reviewing current practice in distribution costing and on attempting to push the frontiers back a little by suggesting some new approaches to overcome previously defined shortcomings.

Fuel measuring and control systems have become progressively more sophisticated as aircraft performance has been extended both in the number of operating regimes and in operational capability. The fuel tank arrangements for the conventional aircraft types of the pre‐supersonic era, both piston and jet‐engined, allowed fairly straight‐forward fuel gauging and management. The tank dispositions were usually in line from left to right across the span of the wing. The advent of the swept wing aircraft introduced the complexities of fore and aft fuel balance in order to limit excursions of the CG about aft of the centre of lift. At the same time the operating economics of both military and civil aircraft, with massive fuel rate demand, required the development of fuel management systems capable of measuring and indicating fuel consumption and quantities to higher orders of accuracy.

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 pressure control valve is a possible means of overcoming the effects of compliance between a hydraulic servo and its load. The valve consists of two stages; an open‐centre flow control valve schematically analogous to a resistance bridge, and a split‐slider valve. In order to study the dynamics of the system it is convenient to set up an electrical analogue for the mechanical system. This will give the non‐linear equations of the system. Several forms of the various impedance elements making up the system require consideration. The resistance of a length of hydraulic line can be obtained from the friction factor and will depend on the flow regime which prevails. In developing an expression for the inductance of a length of line the assumption is made that the wavelength of the oscillatory motion is long compared with the line length. In considering the resistance of orifices it is necessary to take into account the three regimes for flow through an orifice, laminar, transition, and turbulent flow. The inductive effect of an orifice arises from the acceleration of the fluid as the streamlines converge through the orifice; an expression can be derived by applying Newton's second law of motion to the column of oil passing through the orifice. The effective capacitance of a volume can be derived by considering wave motion in one dimension. An expression for the radiation resistance of a piston is derived, and also one for the incident and reflected waves. In constructing the electrical analogue for the slider valve the mass and viscous damping of the slider as well as Bernoulli forces must be represented.

The purpose of this paper is to propose strategies for satellite cluster non‐coplanar orbit transfer to reduce fuel cost of formation maintenance and orbit maneuver.

This research tries to use geometric method model to describe the relative motion of satellites in the cluster non‐coplanar orbit transfer, and genetic algorithm (GA) to optimize the proposed maneuver strategies.

Compared with the C‐W equations, the geometric method model is found to be more precise. Three strategies are proposed and optimized to maintain the relative orbit and a strategy of indefinite phase and non‐synchronous costs least fuel.

Geometric method model can be used to describe the relative motion of satellite cluster, especially on elliptical orbits considering the effects of perturbation, with a simple form and good accuracy. Fuel cost minimization is one of the most important issues in formation flight mission.

This paper provides dynamics analysis about formation non‐coplanar orbit transfer, which is involved in minor researches.

Excessive fat intake is a problem in the UK and other European countries. Looks at the relationship between dietary fat and body fat and the body′s physiological responses to fatty food. Discusses experimental studies on fat and satiety and high fat hyperphagia.

This paper aims to address the problem of formation control for spacecraft formation in elliptic orbits by using local relative measurements.

A decentralized formation control law is proposed to solve the aforementioned problem. The control law for each spacecraft uses only its relative state with respect to the neighboring spacecraft it can sense. These relative states can be acquired by local relative measurements. The formation control problem is converted to n stabilization problems of a single spacecraft by using algebraic graph theories. The resulting relative motion model is described by a linear time-varying system with uncertain parameters. An optimal guaranteed cost control scheme is subsequently used to obtain the desired control performance.

Numerical simulations show the effectiveness of the proposed formation control law.

The proposed control law can be considered as an alternative to global positioning system-based relative navigation and control system for formation flying missions.

The proposed decentralized formation control architecture needs only local relative measurements. Fuel consumption is considered by using an optimal guaranteed cost control scheme.