Inclination Vectors Research Articles

Fuel-optimal satellite formation reconfiguration method with best passive safety parameters

This paper investigates the problem of satellite formation reconfiguration from the best passive safety parameters while ensuring the minimum fuel cost and desired formation configuration. Based on the relative eccentricity and inclination vectors, a hybrid method is proposed that combines the analytical solution and the genetic algorithm optimization method. It transforms the fuel-optimal conditions into the constraints of optimization model, which theoretically ensures the optimal fuel cost. The proposed hybrid approach is applicable to satellite formation reconfiguration problems with variable relative eccentricity and inclination vectors and passive safety concerns. Compared with the optimal three-impulse strategy and the analytical method in two different reconfiguration scenarios, the proposed method is proven to be more general and has advantages in passive safety performance.

Analytical solution of satellite formation impulsive reconfiguration considering passive safety constraints

To handle the potential collision hazards caused by utilizing original fuel optimal impulsive reconfiguration approach, an analytical impulsive satellite formation reconfiguration method in terms of relative eccentricity and inclination vectors (E/I vectors) considering passive safety constraints is proposed. Firstly, the mechanism why original fuel optimal impulsive reconfiguration approach based on relative E/I vectors may cause unsatisfied collision avoidance constraints is analyzed. The unsatisfied scenarios are divided into two cases, namely, the single impulse is too large case and the middle relative E vector is in passive unsafety region case. Secondly, with respect to the unsatisfied collision avoidance scenarios, corresponding analytical impulsive reconfiguration strategies with passive safety constraints are proposed. Finally, the results of the numerical simulations show that the proposed reconfiguration methods can handle the passive safety constraints.

Design of low-altitude Martian orbits using frequency analysis

Nearly-circular Frozen Orbits (FOs) around axisymmetric bodies – or, quasi-circular Periodic Orbits (POs) around non-axisymmetric bodies – are of primary concern in the design of low-altitude survey missions. Here, we study very low-altitude orbits (down to 50 km) in a high-degree and order model of the Martian gravity field. We apply Prony’s Frequency Analysis (FA) to characterize the time variation of their orbital elements by computing accurate quasi-periodic decompositions of the eccentricity and inclination vectors. An efficient, iterative filtering algorithm, previously applied to lunar orbiters, complements the method and is used to accurately compute the locations of POs/FOs, for a wide range of initial conditions. By defining the ’distance’ of any orbit from the family of POs and using the relative amplitudes of the different components of the motion, we can build ’dynamical fate maps’ that graphically depict the survivability of low-eccentricity, low-altitude orbits at every inclination, and can be used for efficient mission planning. While lowering the altitude generally enhances the effect of tesseral and sectorial gravity harmonics, we find this to have less consequence for low altitude Martian satellites, in contrast with the Lunar case. Hence, a high-degree (≃20th) axisymmetric model is adequate for preliminary mission design at moderate altitudes, but should be complemented at low altitudes by the methods described here. All families of POs and their spectral decompositions can be accurately and effectively computed by continuation in arbitrarily complex Martian gravity models, as our filtering algorithm requires only short integration arcs.

A new fuel-balanced formation keeping reference trajectories planning method

Purpose 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). Design/methodology/approach 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. Findings 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. Research limitations/implications 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. Practical implications 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. Originality/value 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.

Autonomous Formation Keeping of Geostationary Satellites with Regional Navigation Satellites and Dynamics

In this paper, the reduced dynamic autonomous formation control of geostationary-Earth-orbit satellites using Indian Regional Navigation Satellite System observables is presented. Generally, the navigation signal is used to determine the position, velocity, and time kinematically. The kinematic formulation, however, is geometric and vulnerable to data outage and cycle slip. Weak geometry of navigation satellites causes high dilution of precision. In this situation, dynamics can provide the estimates with little degradation in accuracy. This requires combining Indian Regional Navigation Satellite System observables with orbital dynamics of the geostationary-Earth-orbit satellites in an extended Kalman filter setup, resulting in improved position and velocity estimates. Moreover, solar radiation pressure coefficient, ephemeris error, and any other unaccounted minute forces are estimated through an empirical acceleration model, along with receiver clock bias and drift, in a reduced dynamics formulation. Furthermore, it is demonstrated that these position and velocity estimates permit autonomous station and formation keeping of geostationary-Earth-orbit satellites. The classical technique using the sun and moon and solar radiation perturbing accelerations to advantage is used to control eccentricity and inclination vectors of each satellite in the formation. The formation-keeping control maneuvers are performed autonomously, whenever an individual satellite’s eccentricity or inclination limit is exceeded.

Optimal Satellite-Formation Collision-Avoidance Maneuver Based on Relative E/I Vectors

AbstractThe optimal satellite-formation collision-avoidance maneuver problem is investigated in terms of relative eccentricity and inclination vectors (E/I vectors) in relative E/I vectors plane. Using the relative E/I vectors theory and under the relative inclination vector unchanged assumption, first, the fuel-optimal collision-avoidance maneuver problem to maneuver the final target configuration with predefined passive safety parameters using minimal fuel is transferred to the geometrical problem to find the shortest distance from the initial point determined by the current relative eccentricity vector to the hyperbolic curve, which is determined by a predefined passive safety parameter in the relative E/I vectors plane. This case is solved using the Newton interaction method. Second, the optimal collision-avoidance maneuver problem to maneuver the final target configuration having maximum passive safety parameter under limiting fuel constraint is interpreted as the geometrical problem to find the opti...

Cluster flight orbit design method for fractionated spacecraft

PurposeThe purpose of this paper is to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.Design/methodology/approachBased 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.FindingsThe 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.Research limitations/implicationsThe 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.Practical implicationsThe cluster flight orbit design method proposed in this paper can be applied by fractionated spacecraft mission designers to propose potential cluster flight orbit solutions.Originality/valueIn this paper, the relative E/I vectors method is adopted to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.

Improved Iterative Calibration for Triaxial Accelerometers Based on the Optimal Observation

This paper presents an improved iterative nonlinear calibration method in the gravitational field for both low-grade and high-grade triaxial accelerometers. This calibration method assumes the probability density function of a Gaussian distribution for the raw outputs of triaxial accelerometers. A nonlinear criterion function is derived as the maximum likelihood estimation for the calibration parameters and inclination vectors, which is solved by the iterative estimation. First, the calibration parameters, including the scale factors, misalignments, biases and squared coefficients are estimated by the linear least squares method according to the multi-position raw outputs of triaxial accelerometers and the initial inclination vectors. Second, the sequence quadric program method is utilized to solve the nonlinear constrained optimization to update the inclination vectors according to the estimated calibration parameters and raw outputs of the triaxial accelerometers. The initial inclination vectors are supplied by normalizing raw outputs of triaxial accelerometers at different positions without any a priori knowledge. To overcome the imperfections of models, the optimal observation scheme is designed according to some maximum sensitivity principle. Simulation and experiments show good estimation accuracy for calibration parameters and inclination vectors.

Optimal satellite formation reconfiguration strategy based on relative orbital elements

This paper presents an analytical fuel-optimal impulsive formation reconfiguration strategy in terms of relative orbital elements (especially using the geometrically intuitive form called relative eccentricity and inclination vectors [E/I vectors]). The relative motion and orbit transfer problem is reparameterized in the form of relative orbit elements. Given a set of transfer conditions, the optimal impulsive strategy for a single satellite maneuver is formulated. Based on the analytical solution of a single satellite transfer, the proposed method is further extended to reconfiguration maneuvers for satellites flying in formation, which accounts for the optimization that relates to the satellites reassignment problem in the reconfiguration stage. Simulations are conducted to demonstrate the validity of the proposed approaches for both single satellite and formation flying reconfiguration scenarios.

The Hoede–Bakker Index Modified to the Shapley–Shubik and Holler–Packel Indices

We present some modifications of the Hoede–Bakker index defined in a social network in which players may influence each other. Due to influences of the other actors, the final decision of a player may be different from his original inclination. The modifications presented in the paper are defined for an arbitrary probability distribution over all inclination vectors. In particular, they concern the situation in which the inclination vectors may be not equally probable. Furthermore, by assuming special probability distributions over all inclination vectors, we construct modifications of the Hoede–Bakker index that coincide with the Shapley–Shubik index and with the Holler–Packel index, respectively. We present a practical example in which the concepts in question are applied to Dutch parties, and a theoretical example in which we show how the modifications can be calculated.

Modifying the Hoede-Bakker Index to the Shapley-Shubik and Holler-Packel Indices

In the paper, we present some modifications of the Hoede-Bakker index defined in a social network in which players may influence each other. Due to influences of the other actors, the final decision of a player may be different from his original inclination. These modifications are defined for an arbitrary probability distribution over all inclination vectors. In particular, they concern a situation in which the inclination vectors may be not equally probable. Furthermore, by assuming special probability distributions over all inclination vectors, we construct modifications of the Hoede-Bakker index that coincide with the Shapley-Shubik index and with the Holler-Packel index, respectively.

Tectonic implications of Paleomagnetic data from the Northland ophiolite, New Zealand

Paleomagnetic sampling of 12 sites from two separate massifs of the Northland ophiolite, New Zealand, yields consistent results. Two characteristic NRM directions are recognised: one of normal polarity associated with weakly magnetised rocks (particularly intrusive dolerites), and another of reversed polarity associated with strongly magnetised rocks (particularly basaltic pillow lavas). Thermal and AF demagnetisation shows that the normal directions are due to a secondary viscous component which reflects the present-day field direction, whilst the reversed directions are stable (typically to 500°C) reflecting either the primary TRM or a hard secondary component. The declination and inclination of this stable magnetisation differ substantially from that of the present-day field implying significant tectonic movement or deformation of the ophiolite since formation. Anomalous declinations and inclinations are interpreted here in terms of rotations about vertical axes and, tentatively, latitudinal translation since no widespread significant tilting has been recognised within the massifs. Declinations are consistent with clockwise rotations of 50° and 120° for the Cape Reinga and Mangakahia massifs, respectively, probably associated with obduction at a convergent margin with a right-lateral slip component, situated to the northeast of Northland. The anomalously low inclination vectors (30–40°) are consistent with an origin at lower than present latitudes which, if true, implies long-lived N-S translation of oceanic crust in the southwest Pacific region between Cretaceous and Oligocene times.