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1
Chen, Q., J. D. Meiss, and I. C. Percival. "Orbit extension method for finding unstable orbits." Physica D: Nonlinear Phenomena 29, no. 1-2 (November 1987): 143–54. http://dx.doi.org/10.1016/0167-2789(87)90051-0.
Testo completo
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Song, Xu Min, Yong Chen, and Qi Lin. "Orbit Plan Method for General Rendezvous Problems." Applied Mechanics and Materials 543-547 (March 2014): 1385–88. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1385.
Testo completoAbstract (sommario):
The orbit plan method of rendezvous mission was studied in this paper. We are concerned with the general rendezvous problem between two satellites which may be in non-coplanar, eccentric orbits, considering orbit perturbation and rendezvous time limitation. The planning problem was modeled as a nonlinear optimization problem, and the adaptive simulated annealing method was used to get the global solution. The Lambert algorithm was used to compute the transfer orbit, so that the endpoint constraint of rendezvous was eliminated. A shooting technique was used to solve the perturbed lambert problem. The method was validated by simulation results.
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Wang, Qianxin, Chao Hu, and Ya Mao. "Correction Method for the Observed Global Navigation Satellite System Ultra-Rapid Orbit Based on Dilution of Precision Values." Sensors 18, no. 11 (November 12, 2018): 3900. http://dx.doi.org/10.3390/s18113900.
Testo completoAbstract (sommario):
For ultra-rapid orbits provided by the Global Navigation Satellite System (GNSS), the key parameters, accuracy and timeliness, must be taken into consideration in real-time and near real-time applications. However, insufficient observations in later epochs appear to generate low accuracy in observed orbits, for which a correlation between the Dilution of Precision (DOP) of the orbit parameters and their accuracy is found. To correct the observed GNSS ultra-rapid orbit, a correction method based on the DOP values is proposed by building the function models between DOP values and the orbit accuracy. With 10-day orbit determination experiments, the results show that the observed ultra-rapid-orbit errors, generated by insufficient observations, can be corrected by 12–22% for the last three hours of the observed orbits. Moreover, considering the timeliness constraints in ultra-rapid-orbit determination, a DOP amplification factor is defined to weight the contribution of each tracking station and optimize the station distribution in the orbit determination procedure. Finally, six schemes are designed to verify the method and strategy in determining the ultra-rapid orbit based on one-month observations. The orbit accuracy is found to decrease by 1.27–6.34 cm with increasing amplification factor from 5–20%. Thus, the observed ultra-orbit correction method proposed is ideal when considering accuracy and timeliness in ultra-rapid orbit determination.
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Zhang, Mingjie, Jiangang Yang, Wanfu Zhang, and Qianlei Gu. "Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals." Applied Sciences 11, no. 9 (May 7, 2021): 4237. http://dx.doi.org/10.3390/app11094237.
Testo completoAbstract (sommario):
The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.
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Feng, Jingjing, Qichang Zhang, Wei Wang, and Shuying Hao. "A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method." Mathematical Problems in Engineering 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/8585290.
Testo completoAbstract (sommario):
In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.
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Ye, Fei, Yunbin Yuan, Bingfeng Tan, Zhiguo Deng, and Jikun Ou. "The Preliminary Results for Five-System Ultra-Rapid Precise Orbit Determination of the One-Step Method Based on the Double-Difference Observation Model." Remote Sensing 11, no. 1 (December 29, 2018): 46. http://dx.doi.org/10.3390/rs11010046.
Testo completoAbstract (sommario):
The predicted parts of ultra-rapid orbits are important for (near) real-time Global Navigation Satellite System (GNSS) precise applications; and there is little research on GPS/GLONASS/BDS/Galileo/QZSS five-system ultra-rapid precise orbit determination; based on the one-step method and double-difference observation model. However; the successful development of a software platform for solving five-system ultra-rapid orbits is the basis of determining and analyzing these orbits. Besides this; the different observation models and processing strategies facilitate to validate the reliability of the various ultra-rapid orbits. In this contribution; this paper derives the double-difference observation model of five-system ultra-rapid precise orbit determination; based on a one-step method; and embeds this method and model into Bernese v5.2; thereby forming a new prototype software platform. For validation purposes; 31 days of real tracking data; collected from 130 globally-distributed International GNSS Service (IGS) multi-GNSS Experiment (MGEX) stations; are used to determine a five-system ultra-rapid precise orbit. The performance of the software platform is evaluated by analysis of the orbit discontinuities at day boundaries and by comparing the consistency with the MGEX orbits from the Deutsches GeoForschungsZentrum (GFZ); between the results of this new prototype software platform and the ultra-rapid orbit provided by the International GNSS Monitoring and Assessment System (iGMAS) analysis center (AC) at the Institute of Geodesy and Geophysics (IGG). The test results show that the average standard deviations of orbit discontinuities in the three-dimension direction are 0.022; 0.031; 0.139; 0.064; 0.028; and 0.465 m for GPS; GLONASS; BDS Inclined Geosynchronous Orbit (IGSO); BDS Mid-Earth Orbit (MEO); Galileo; and QZSS satellites; respectively. In addition; the preliminary results of the new prototype software platform show that the consistency of this platform has been significantly improved compared to the software package of the IGGAC.
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Qin, Huang, Zhang, Wang, Yan, Xie, Cao, and Wang. "Precise Orbit Determination for BeiDou GEO/IGSO Satellites during Orbit Maneuvering with Pseudo-Stochastic Pulses." Remote Sensing 11, no. 21 (November 4, 2019): 2587. http://dx.doi.org/10.3390/rs11212587.
Testo completoAbstract (sommario):
In order to provide better service for the Asia-Pacific region, the BeiDou navigation satellite system (BDS) is designed as a constellation containing medium earth orbit (MEO), geostationary earth orbit (GEO), and inclined geosynchronous orbit (IGSO). However, the multi-orbit configuration brings great challenges for orbit determination. When orbit maneuvering, the orbital elements of the maneuvered satellites from broadcast ephemeris are unusable for several hours, which makes it difficult to estimate the initial orbit in the process of precise orbit determination. In addition, the maneuvered force information is unknown, which brings systematic orbit integral errors. In order to avoid these errors, observation data are removed from the iterative adjustment. For the above reasons, the precise orbit products of maneuvered satellites are missing from IGS (international GNSS (Global Navigation Satellite System) service) and iGMAS (international GNSS monitoring and assessment system). This study proposes a method to determine the precise orbits of maneuvered satellites for BeiDou GEO and IGSO. The initial orbits of maneuvered satellites could be backward forecasted according to the precise orbit products. The systematic errors caused by unmodeled maneuvered force are absorbed by estimated pseudo-stochastic pulses. The proposed method for determining the precise orbits of maneuvered satellites is validated by analyzing data of stations from the Multi-GNSS Experiment (MGEX). The results show that the precise orbits of maneuvered satellites can be estimated correctly when orbit maneuvering, which could supplement the precise products from the analysis centers of IGS and iGMAS. It can significantly improve the integrality and continuity of the precise products and subsequently provide better precise products for users.
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OLDEMAN, BART E., ALAN R. CHAMPNEYS, and BERND KRAUSKOPF. "HOMOCLINIC BRANCH SWITCHING: A NUMERICAL IMPLEMENTATION OF LIN'S METHOD." International Journal of Bifurcation and Chaos 13, no. 10 (October 2003): 2977–99. http://dx.doi.org/10.1142/s0218127403008326.
Testo completoAbstract (sommario):
We present a numerical method for branch switching between homoclinic orbits to equilibria of ODEs computed via numerical continuation. Starting from a 1-homoclinic orbit our method allows us to find and follow an N-homoclinic orbit, for any N>1 (if it exists nearby). This scheme is based on Lin's method and it is robust and reliable. The method is implemented in AUTO/HOMCONT. A system of ordinary differential equations introduced by Sandstede featuring inclination and orbit flip bifurcations and homoclinic-doubling cascades, is used as a test bed for the algorithm. It is also successfully applied to reliably find multihump traveling wave solutions in the FitzHugh–Nagumo nerve-axon equations and in a fourth-order Hamiltonian system arising as a model for water waves.
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Kong, Qiaoli, Fan Gao, Jinyun Guo, Litao Han, Linggang Zhang, and Yi Shen. "Analysis of Precise Orbit Predictions for a Hy-2A Satellite with Three Atmospheric Density Models Based on Dynamic Method." Remote Sensing 11, no. 1 (December 27, 2018): 40. http://dx.doi.org/10.3390/rs11010040.
Testo completoAbstract (sommario):
HY-2A (Haiyang 2A) is the first altimetry satellite in China, and it was designed to be in a repeated ground track orbit to achieve the mission targets. Maneuvers are necessary to keep the satellite on the designed orbit according to the dynamic precise orbital prediction. Atmospheric density models are essential for predicting the low Earth orbit (LEO) satellites, such as HY-2A. Nevertheless, it is a complex process to determine the optimal atmospheric density model for orbit prediction. In this paper, short-term and long-term orbit predictions based on the dynamic method using three different atmospheric density models are tested. Detailed comparisons and evaluation of the accuracy of the predicted results are performed. Furthermore, to assess the results for the ground tracking of the satellite, the interpolation method especially for a spherical surface is introduced. The results show that among the three models, the Jacchia 1971 model is in the closest agreement with Multi-Mission Ground Segment for Altimetry precise positioning and Orbitography (SSALTO) precise orbits. The root-mean-squares (RMSs) of radial orbit differences between the predicted and precise orbits are 0.016 m, 0.091 m, 0.176 m, 0.573 m, and 1.421 m for predicted 1-h, 12-h, 1-day, 3-day, and 7-day arcs, respectively.
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Lu, Qiuying, and Vincent Naudot. "Bifurcation Complexity from Orbit-Flip Homoclinic Orbit of Weak Type." International Journal of Bifurcation and Chaos 26, no. 04 (April 2016): 1650059. http://dx.doi.org/10.1142/s0218127416500590.
Testo completoAbstract (sommario):
In this paper, we study the unfolding of a three-dimensional vector field having an orbit-flip homoclinic orbit of weak type. Such a homoclinic orbit is a degenerate version of the so-called orbit-flip homoclinic orbit. We show the existence of inclination-flip homoclinic orbits of arbitrary higher order bifurcating from the unperturbed system. Our strategy consists of using the local moving coordinates method and blow up in the parameter space. In addition, the numerical existence of the orbit-flip homoclinic orbit of weak type is presented based on the truncated Taylor expansion and the numerical computation for both the strong stable manifold and unstable manifold.
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Ge, Haibo, Bofeng Li, Maorong Ge, Liangwei Nie, and Harald Schuh. "Improving Low Earth Orbit (LEO) Prediction with Accelerometer Data." Remote Sensing 12, no. 10 (May 17, 2020): 1599. http://dx.doi.org/10.3390/rs12101599.
Testo completoAbstract (sommario):
Low Earth Orbit (LEO) satellites have been widely used in scientific fields or commercial applications in recent decades. The demands of the real time scientific research or real time applications require real time precise LEO orbits. Usually, the predicted orbit is one of the solutions for real time users, so it is of great importance to investigate LEO orbit prediction for users who need real time LEO orbits. The centimeter level precision orbit is needed for high precision applications. Aiming at obtaining the predicted LEO orbit with centimeter precision, this article demonstrates the traditional method to conduct orbit prediction and put forward an idea of LEO orbit prediction by using onboard accelerometer data for real time applications. The procedure of LEO orbit prediction is proposed after comparing three different estimation strategies of retrieving initial conditions and dynamic parameters. Three strategies are estimating empirical coefficients every one cycle per revolution, which is the traditional method, estimating calibration parameters of one bias of accelerometer hourly for each direction by using accelerometer data, and estimating calibration parameters of one bias and one scale factor of the accelerometer for each direction with one arc by using accelerometer data. The results show that the predicted LEO orbit precision by using the traditional method can reach 10 cm when the predicted time is shorter than 20 min, while the predicted LEO orbit with better than 5 cm for each orbit direction can be achieved with accelerometer data even to predict one hour.
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Alpatov, A. P., and Yu M. Goldshtein. "Assessment perspectives for the orbital utilization of space debris." Kosmìčna nauka ì tehnologìâ 27, no. 3 (July 2021): 3–12. http://dx.doi.org/10.15407/knit2021.03.003.
Testo completoAbstract (sommario):
Technogenic pollution of the near-Earth space by fragments of space debris of various sizes significantly limits the possibilities for implementing space activities and represents a great danger to objects on Earth. Low orbits with heights up to 2000 km are particularly heavily clogged. The Inter-Agency Space Debris Coordination Committee recommends removing fragments of space debris from the area of working orbits. Currently, promising ways of space debris removing are considered: descent into the Earth’s atmosphere, relocation to an orbit with a lifetime less than twenty-five years, relocation to an utilization orbit, and orbital disposal. Orbital utilization considers space debris as a resource for the industry in orbit. The objectives of the article are to assess the perspectives for the orbital utilization of space debris and to develop a method for choosing the number and placement of safe recycling orbits in the area of low near-Earth orbits. The paper analyses the prospects for the use of orbital utilization of space debris and the assessment of the possibilities of using orbital storage and subsequent reuse of dismantled space objects, instruments and materials. A number of problems of planning and organizing the orbital utilization of space debris are formulated and solved. A method for determining safe orbits of space debris utilization in the area of low near-Earth orbits based on a criteria system developed. Using the developed method and software package, the possible orbits of space debris utilization in the area of low near-Earth orbits are determined. The lifetime of a space object in the utilization orbit, the stability of the orbit of the utilization at a long time interval, and the energy consumptions for transferring the space object from the working orbit to the utilization orbit are estimated. The novelty of the obtained results consists in the development of a clustering technique for the orbits of utilized space debris objects and the development of a technique for selecting a possible orbit for the utilization of space debris in the area of low near-Earth orbits. The results obtained can be used in the planning and organization of the orbital utilization of space debris.
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Kuang, Wentian, and Duokui Yan. "Existence of Prograde Double-Double Orbits in the Equal-Mass Four-Body Problem." Advanced Nonlinear Studies 18, no. 4 (November 1, 2018): 819–43. http://dx.doi.org/10.1515/ans-2018-0009.
Testo completoAbstract (sommario):
AbstractBy introducing simple topological constraints and applying a binary decomposition method, we show the existence of a set of prograde double-double orbits for any rotation angle {\theta\in(0,\pi/7]} in the equal-mass four-body problem. A new geometric argument is introduced to show that for any {\theta\in(0,\pi/2)}, the action of the minimizer corresponding to the prograde double-double orbit is strictly greater than the action of the minimizer corresponding to the retrograde double-double orbit. This geometric argument can also be applied to study orbits in the planar three-body problem, such as the retrograde orbits, the prograde orbits, the Schubart orbit and the Hénon orbit.
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Yue, Xiaokui, Xuechuan Wang, and Honghua Dai. "A Simple Time Domain Collocation Method to Precisely Search for the Periodic Orbits of Satellite Relative Motion." Mathematical Problems in Engineering 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/854967.
Testo completoAbstract (sommario):
A numerical approach for obtaining periodic orbits of satellite relative motion is proposed, based on using the time domain collocation (TDC) method to search for the periodic solutions of an exactJ2nonlinear relative model. The initial conditions for periodic relative orbits of the Clohessy-Wiltshire (C-W) equations or Tschauner-Hempel (T-H) equations can be refined with this approach to generate nearly bounded orbits. With these orbits, a method based on the least-squares principle is then proposed to generate projected closed orbit (PCO), which is a reference for the relative motion control. Numerical simulations reveal that the presented TDC searching scheme is effective and simple, and the projected closed orbit is very fuel saving.
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Qi, Naiming, Mingying Huo, and Qiufan Yuan. "Displaced Electric Sail Orbits Design and Transition Trajectory Optimization." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/932190.
Testo completoAbstract (sommario):
Displaced orbits for spacecraft propelled by electric sails are investigated as an alternative to the use of solar sails. The orbital dynamics of electric sails based spacecraft are studied within a spherical coordinate system, which permits finding the solutions of displaced electric sail orbits and optimize transfer trajectory. Transfer trajectories from Earth's orbit to displaced orbit are also studied in an optimal framework, by using genetic algorithm and Gauss pseudospectral method. The initial guesses for the state and control histories used in the Gauss pseudospectral method are interpolated from the best solution of a genetic algorithm. Numerical simulations show that the electric sail is able to perform the transfer from Earth’s orbit to displaced orbit in acceptable time, and the hybrid optimization method has the capability to search the feasible and optimal solution without any initial value guess.
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Emami, M., and O. Naserian. "New large sets of t-designs from t-homogeneous groups." Discrete Mathematics, Algorithms and Applications 10, no. 04 (July 30, 2018): 1850051. http://dx.doi.org/10.1142/s1793830918500519.
Testo completoAbstract (sommario):
One of the most common direct methods for constructing [Formula: see text]-designs and large sets of [Formula: see text]-designs is assembling orbits obtained from the action of a permutation group [Formula: see text] on the set of all [Formula: see text]-subsets of a [Formula: see text]-set. It is well known that when G is a [Formula: see text]-homogeneous group, then each orbit is a [Formula: see text]-design. Therefore the problem is that how one could assemble these orbits to make [Formula: see text]-designs with the same index to construct a large set of [Formula: see text]-designs. The case where the orbit sizes are limited up to two values is already investigated. Here, we present a generalization of this method to assemble the set of orbits when the orbit sizes are limited up to three values. Meanwhile, as an example of this method, we construct the large sets [Formula: see text] for [Formula: see text] two of them are new.
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Potu, Shirish, S. K. Anand, and Soumyendu Raha. "Robust Initial Satellite Orbit Determination method using a Modified Kalman Filter." Journal of Navigation 72, no. 3 (January 28, 2019): 528–38. http://dx.doi.org/10.1017/s0373463318001042.
Testo completoAbstract (sommario):
The control segment in satellite navigation systems is responsible for estimating satellite orbit and clock bias which is required for a reliable Position, Navigation and Timing (PNT) user service. Initial orbit determination is a crucial step which accounts for all unknowns/anomalous parameters such as satellite orbit manoeuvres, on board and receiver clock frequency variations and environmental effects. It is vital that the estimates of the orbits and clock are insensitive to these factors. In this paper, an initial orbit determination method is presented using existing robust methodology for estimation of initial satellite position and its propagation using a variant of the Kalman Filter (KF) which allows the initial position determination process to be independent of satellite and receiver anomalies. The derivation of this KF variant is presented. Preliminary results obtained from simulated data are shown. The said method is checked for robustness by comparing results obtained for a given satellite position data set with that from the conventional Kalman Filter. The conventional KF exhibits divergence due to anomalies which are eliminated by the use of the method presented in this paper.
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XU, YANCONG, DEMING ZHU, and FENGJIE GENG. "CODIMENSION 3 HETEROCLINIC BIFURCATIONS WITH ORBIT AND INCLINATION FLIPS IN REVERSIBLE SYSTEMS." International Journal of Bifurcation and Chaos 18, no. 12 (December 2008): 3689–701. http://dx.doi.org/10.1142/s0218127408022652.
Testo completoAbstract (sommario):
Heteroclinic bifurcations with orbit-flips and inclination-flips are investigated in a four-dimensional reversible system by using the method originally established in [Zhu, 1998; Zhu & Xia, 1998]. The existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic orbit, R-symmetric homoclinic orbit and R-symmetric periodic orbit are obtained. The double R-symmetric homoclinic bifurcation is found, and the continuum of R-symmetric periodic orbits accumulating into a homoclinic orbit is also demonstrated. Moreover, the bifurcation surfaces and the existence regions are given, and the corresponding bifurcation diagrams are drawn.
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Dabrowski, Pawel S. "The Symmetry of GPS Orbit Ascending Nodes." Remote Sensing 13, no. 3 (January 22, 2021): 387. http://dx.doi.org/10.3390/rs13030387.
Testo completoAbstract (sommario):
Theoretical nominal GPS orbits are parallel and share six ascending nodes of orbital planes. However, due to the perturbations and continuous modernization of the system, this state does not occur. The configuration of satellite orbits is continuously monitored by the control segment and presented regularly in the form of a GPS almanac. Almanacs, however, do not contain a parameter defining the convergence of orbits. This work presents a novel method of assessment of the configuration of orbit ascending nodes compared with the nominal constellation state. The method is a tool for space segment monitoring and detection of anomalies. The source data were 7035 System Effectiveness Model almanacs published from the 847th to 2123rd GPS weeks (March 1996–September 2020). The algorithm uses the procedure of assigning satellites to orbital planes and both the robust estimation and the least-squares methods to determine the estimates of the angular separation of orbit ascending nodes. A long-term analysis of the symmetry and trend of changes in the position of the ascending nodes was conducted. The study showed the occurrence of significant anomalies. The research provides information on the trend of satellite orbit separations and deviations of orbital planes from the initial hexagonal GPS symmetry.
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Yu, Sunkyoung, Donguk Kim, Junesol Song, and Changdon Kee. "Covariance Analysis of Real-Time Precise GPS Orbit Estimated from Double-Differenced Carrier Phase Observations." Remote Sensing 11, no. 19 (September 28, 2019): 2271. http://dx.doi.org/10.3390/rs11192271.
Testo completoAbstract (sommario):
The covariance of real-time global positioning system (GPS) orbits has been drawing attention in various fields such as user integrity, navigation performance improvement, and fault detection. The international global navigation satellite system (GNSS) service (IGS) provides real-time orbit standard deviations without correlations between the axes. However, without correlation information, the provided covariance cannot assure the performance of the orbit product, which would, in turn, causes significant problems in fault detection and user integrity. Therefore, we studied real-time GPS orbit covariance characteristics along various coordinates to effectively provide conservative covariance. To this end, the covariance and precise orbits are estimated by means of an extended Kalman filter using double-differenced carrier phase observations of 61 IGS reference stations. Furthermore, we propose a new method for providing covariance to minimize loss of correlation. The method adopted by the IGS, which neglects correlation, requires 4.5 times the size of the covariance to bind orbit errors. By comparison, our proposed method reduces this size from 4.5 to 1.3 using only one additional parameter. In conclusion, the proposed method effectively provides covariance to users.
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Corney, Stuart. "Control of Chaos in the Rössler System." Australian Journal of Physics 50, no. 2 (1997): 263. http://dx.doi.org/10.1071/p96015.
Testo completoAbstract (sommario):
The control method of Ott, Grebogi and Yorke (1990) as applied to the Rössler system, a set of three-dimensional non-linear differential equations, is examined. Using numerical time series data for a single dynamical variable the method was successfully employed to control several of the unstable periodic orbits in a three-dimensional embedding of the data. The method also failed for a number of unstable periodic orbits due to difficulties in linearising about the orbit or the tangential coincidence of the stable manifold and the motion of the orbit with external parameter.
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Zhu, Ling, Glenn van de Ven, Ryan Leaman, Robert J. J. Grand, Jesús Falcón-Barroso, Prashin Jethwa, Laura L. Watkins, et al. "Disentangling the formation history of galaxies via population-orbit superposition: method validation." Monthly Notices of the Royal Astronomical Society 496, no. 2 (June 6, 2020): 1579–97. http://dx.doi.org/10.1093/mnras/staa1584.
Testo completoAbstract (sommario):
ABSTRACT We present population-orbit superposition models for external galaxies based on Schwarzschild’s orbit-superposition method, by tagging the orbits with age and metallicity. The models fit the density distributions, kinematic, and age and metallicity maps from integral field unit (IFU) spectroscopy observations. We validate the method and demonstrate its power by applying it to mock data, similar to those obtained by the Multi-Unit Spectroscopic Explorer (MUSE) IFU on the Very Large Telescope (VLT). These mock data are created from Auriga galaxy simulations, viewed at three different inclination angles (ϑ = 40°, 60°, 80°). Constrained by MUSE-like mock data, our model can recover the galaxy’s stellar orbit distribution projected in orbital circularity λz versus radius r, the intrinsic stellar population distribution in age t versus metallicity Z, and the correlation between orbits’ circularity λz and stellar age t. A physically motivated age–metallicity relation improves the recovering of intrinsic stellar population distributions. We decompose galaxies into cold, warm, and hot+counter-rotating components based on their orbit circularity distribution, and find that the surface density, velocity, velocity dispersion, and age and metallicity maps of each component from our models well reproduce those from simulation, especially for projections close to edge-on. These galaxies exhibit strong global age versus σz relation, which is well recovered by our model. The method has the power to reveal the detailed build-up of stellar structures in galaxies, and offers a complement to local resolved, and high-redshift studies of galaxy evolution.
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Bai, Xiaoli, and John L. Junkins. "Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits." Mathematical Problems in Engineering 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/926158.
Testo completoAbstract (sommario):
The halo orbits around the Earth-MoonL2libration point provide a great candidate orbit for a lunar communication satellite, where the satellite remains above the horizon on the far side of the Moon being visible from the Earth at all times. Such orbits are generally unstable, and station-keeping strategies are required to control the satellite to remain close to the reference orbit. A recently developed Modified Chebyshev-Picard Iteration method is used to compute corrective maneuvers at discrete time intervals for station-keeping of halo orbit satellite, and several key parameters affecting the mission performance are analyzed through numerical simulations. Compared with previously published results, the presented method provides a computationally efficient station-keeping approach which has a simple control structure that does not require weight turning and, most importantly, does not need state transition matrix or gradient information computation. The performance of the presented approach is shown to be comparable with published methods.
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DOERNER, R., B. HÜBINGER, and W. MARTIENSSEN. "ADAPTIVE ORBIT CORRECTION IN CHAOS CONTROL." International Journal of Bifurcation and Chaos 05, no. 04 (August 1995): 1175–79. http://dx.doi.org/10.1142/s0218127495000831.
Testo completoAbstract (sommario):
The deterministic chaotic motion of a nonlinear system is governed by the set of unstable periodic orbits constituting the strange attractor. We introduce an adaptation scheme to improve experimentally the coordinates of orbits calculated from an approximate model or extracted from a time series. The method also allows to trace an unstable orbit if the system parameters are slowly changing. Feasibility of the method is demonstrated by numerical simulation at the Hénon system using the OGY control method, and experimentally at a driven pendulum using the local control method.
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DIMINNIE, DAVID C., and RICHARD HABERMAN. "ACTION AND PERIOD OF HOMOCLINIC AND PERIODIC ORBITS FOR THE UNFOLDING OF A SADDLE-CENTER BIFURCATION." International Journal of Bifurcation and Chaos 13, no. 11 (November 2003): 3519–30. http://dx.doi.org/10.1142/s0218127403008569.
Testo completoAbstract (sommario):
At a saddle-center bifurcation for Hamiltonian systems, the homoclinic orbit is cusp shaped at the nonlinear nonhyperbolic saddle point. Near but before the bifurcation, orbits are periodic corresponding to the unfolding of the homoclinic orbit, while after the bifurcation a double homoclinic orbit is formed with a local and global branch. The saddle-center bifurcation is dynamically unfolded due to a slowly varying potential. Near the unfolding of the homoclinic orbit, the period and action are analyzed. Asymptotic expansions for the action, period and dissipation are obtained in an overlap region near the homoclinic orbit of the saddle-center bifurcation. In addition, the unfoldings of the action and dissipation functions associated with zero energy orbits (periodic and homoclinic) near the saddle-center bifurcation are determined using the method of matched asymptotic expansions for integrals.
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Lun, D. R., M. Eberspächer, K. Amos, W. Scheid, and S. J. Buckman. "Improved spin-orbit inversion method." Physical Review A 58, no. 6 (December 1, 1998): 4993–96. http://dx.doi.org/10.1103/physreva.58.4993.
Testo completo
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Lipnitsky, V. A., and S. I. Semyonov. "Error correction by Reed–Solomon codes using its automorphisms." Proceedings of the National Academy of Sciences of Belarus, Physical-Technical Series 66, no. 1 (April 2, 2021): 110–16. http://dx.doi.org/10.29235/1561-8358-2021-66-1-110-116.
Testo completoAbstract (sommario):
The article explores the syndrome invariants of АГ-group of automorphisms of Reed–Solomon codes (RS-codes) that are a joint group of affine and cyclic permutations. The found real invariants are a set of norms of N Г-orbits that make up one or another АГ-orbit. The norms of Г-orbits are vectors with 2 1 Cδ− coordinates from the Galois field, that are determined by all kinds of pairs of components of the error syndromes. In this form, the invariants of the АГ-orbits were cumbersome and difficult to use. Therefore, their replacement by conditional partial invariants is proposed. These quasi-invariants are called norm-projections. Norm-projection uniquely identifies its АГ-orbit and therefore serves as an adequate way for formulating the error correction method by RS-codes based on АГ-orbits. The power of the АГ-orbits is estimated by the value of N2, equal to the square of the length of the RS-code. The search for error vectors in transmitted messages by a new method is reduced to parsing the АГ‑orbits, but actually their norm-projections, with the subsequent search for these errors within a particular АГ-orbit. Therefore, the proposed method works almost N2 times faster than traditional syndrome methods, operating on the basic of the “syndrome – error” principle, that boils down to parsing the entire set of error vectors until a specific vector is found.
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Nakamura, N., H. Takaki, H. Sakai, M. Satoh, K. Harada, and Y. Kamiya. "New orbit correction method uniting global and local orbit corrections." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 556, no. 2 (January 2006): 421–32. http://dx.doi.org/10.1016/j.nima.2005.11.062.
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GALVANETTO, UGO. "DELAYED FEEDBACK CONTROL OF CHAOTIC SYSTEMS WITH DRY FRICTION." International Journal of Bifurcation and Chaos 12, no. 08 (August 2002): 1877–83. http://dx.doi.org/10.1142/s0218127402005546.
Testo completoAbstract (sommario):
This paper describes some numerical techniques to control unstable periodic orbits embedded in chaotic attractors of a particular discontinuous mechanical system. The control method is a continuous time delayed feedback that modifies the stability of the orbit but does not affect the orbit itself.
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Yan, Duokui, and Tiancheng Ouyang. "New Phenomena in the Spatial Isosceles Three-Body Problem." International Journal of Bifurcation and Chaos 25, no. 09 (August 2015): 1550116. http://dx.doi.org/10.1142/s0218127415501163.
Testo completoAbstract (sommario):
In the three-body problem, it is known that there exists a special set of periodic orbits: spatial isosceles periodic orbits. In each period, one body moves up and down along a straight line, and the other two bodies rotate around this line. In this work, we revisit this set of orbits by applying variational method. Two unexpected phenomena are discovered. First, this set is not always spatial. It actually bifurcates from the circular Euler (central configuration) orbit to the Broucke (collision) orbit. Second, one of the orbits in this set encounters an oscillating behavior. By running its initial condition, the orbit stays periodic for only a few periods before it becomes irregular. However, it moves close to another periodic shape in a while. Shortly it falls apart again and starts running close to a third periodic shape after a moment. This oscillation continues as t increases. Actually, up to t = 1.2 × 105, the orbit is bounded and keeps oscillating between periodic shapes and irregular motions.
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Wang, Qianxin, Chao Hu, and Kefei Zhang. "A BDS-2/BDS-3 Integrated Method for Ultra-Rapid Orbit Determination with the Aid of Precise Satellite Clock Offsets." Remote Sensing 11, no. 15 (July 25, 2019): 1758. http://dx.doi.org/10.3390/rs11151758.
Testo completoAbstract (sommario):
The accuracy of ultra-rapid orbits is a key parameter for the performance of GNSS (Global Navigation Satellite System) real-time or near real-time precise positioning applications. The quality of the current BeiDou demonstration system (BDS) ultra-rapid orbits is lower than that of GPS, especially for the new generational BDS-3 satellites due to the fact that the availability of the number of ground tracking stations is limited, the geographic distribution of these stations is poor, and the data processing strategies adopted are not optimal. In this study, improved data processing strategies for the generation of ultra-rapid orbits of BDS-2/BDS-3 satellites are investigated. This includes both observed and predicted parts of the orbit. First, the predicted clock offsets are taken as constraints in the estimation process to reduce the number of the unknown parameters and improve the accuracy of the parameter estimates of the orbit. To obtain more accurate predicted clock offsets for the BDS’ orbit determination, a denoising method (also called the Tikhonov regularization algorithm), inter-satellite correlation, and the partial least squares method are all incorporated into the clock offsets prediction model. Then, the Akaike information criterion (AIC) is used to determine the arc length in the estimation models by taking the optimal arc length in the estimation of the initial orbit states into consideration. Finally, a number of experiments were conducted to evaluate the performance of the ultra-rapid orbits resulting from the proposed methods. Results showed that: (1) Compared with traditional models, the accuracy improvement of the predicted clock offsets from the proposed methods were 40.5% and 26.1% for BDS-2 and BDS-3, respectively; (2) the observed part of the orbits can be improved 9.2% and 5.0% for BDS-2 and BDS-3, respectively, by using the predicted clock offsets as constraints; (3) the accuracy of the predicted part of the orbits showed a high correlation with the AIC value, and the accuracy of the predicted orbits could be improved up to 82.2%. These results suggest that the approaches proposed in this study can significantly enhance the accuracy of the ultra-rapid orbits of BDS-2/BDS-3 satellites.
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Zhai, Yawei, Jaymin Patel, Xingqun Zhan, Mathieu Joerger, and Boris Pervan. "An Advanced Receiver Autonomous Integrity Monitoring (ARAIM) Ground Monitor Design to Estimate Satellite Orbits and Clocks." Journal of Navigation 73, no. 5 (April 28, 2020): 1087–105. http://dx.doi.org/10.1017/s0373463320000181.
Testo completoAbstract (sommario):
This paper describes a method to determine global navigation satellite systems (GNSS) satellite orbits and clocks for advanced receiver autonomous integrity monitoring (ARAIM). The orbit and clock estimates will be used as a reference truth to monitor signal-in-space integrity parameters of the ARAIM integrity support message (ISM). Unlike publicly available orbit and clock products, which aim to maximise estimation accuracy, a straightforward and transparent approach is employed to facilitate integrity evaluation. The proposed monitor is comprised of a worldwide network of sparsely distributed reference stations and will employ parametric satellite orbit models. Two separate analyses, covariance analysis and model fidelity evaluation, are carried out to assess the impact of measurement errors and orbit model uncertainty on the estimated orbits and clocks, respectively. The results indicate that a standard deviation of 30 cm can be achieved for the estimated orbit/clock error, which is adequate for ISM validation.
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Ye, Fei, Yunbin Yuan, Baocheng Zhang, Bingfeng Tan, and Jikun Ou. "A Three-Step Method for Determining Unhealthy Time Period of GPS Satellite Orbit in Broadcast Ephemeris and Its Preliminary Applications for Precise Orbit Determination." Remote Sensing 11, no. 9 (May 8, 2019): 1098. http://dx.doi.org/10.3390/rs11091098.
Testo completoAbstract (sommario):
Abnormal information of satellite orbits inevitably appears in the broadcast ephemeris. Failure to obtain unhealthy information on GPS satellite orbits in precise orbit determination (POD) degrades GPS service performance. At present, the reliable unhealthy information published by the Center for Orbit Determination in Europe (CODE) is usually used, but it has at least one-day latency, and the current level of unhealthy information cannot fully meet the requirements of rapid and real-time geodetic applications, especially for non-IGS (International global navigation satellite systems (GNSS) Service) analysis centers and BeiDou navigation satellite system (BDS) users. Furthermore, the unhealthy orbit information detected by the traditional method, which is based on the synchronized pseudo-range residuals and regional observation network, cannot meet the requirement of setting separate sub-arcs in POD. In view of these problems, we propose a three-step method for determining unhealthy time periods of GPS satellite orbit in broadcast ephemeris during POD to provide reliable unhealthy information in near-real time. This method is a single-epoch solution, and it can detect unhealthy time periods in each sampling of observation in theory. It was subsequently used to detect unhealthy time periods for satellites G09 and G01 based on the 111 globally distributed tracking stations in the IGS. The performance of the new method was evaluated using cross-validation. Based on the test results, it detected an orbital leap for G09 in the broadcast ephemeris from 09:59:42 to 14:00:42 on 25 August 2017. Compared to the traditional method, the unhealthy start time using the three-step method was in better agreement with the information provided by CODE’s satellite crux files. G01 did not appear to have an orbital leap on the specified date, but it was misjudged by the traditional method. Furthermore, compared to the traditional method, the three-step method can perform unhealthy time period detection for a satellite all day long. In addition, precise orbit determination for unhealthy satellites is realized successfully with the unhealthy orbit arc information identified in this study. Compared to the CODE orbit, the root mean square and standard deviation of the new method for G09 are less than 2 cm, and the three-step method shows an improvement in accuracy compared with the traditional method. From the above results, it can be seen that this study can provide a feasible approach to meet the real-time unhealthy time period detection requirements of a satellite orbit in a broadcast ephemeris during POD. Furthermore, compared to waiting for updates of CODE’s satellite crux files or for accumulating delayed observation data, it has the potential to provide additional information in the process of generating ultra-rapid/real-time orbits.
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Li, Kai, Xuhua Zhou, Wenbin Wang, Yang Gao, Gang Zhao, Enzhe Tao, and Kexin Xu. "Centimeter-Level Orbit Determination for TG02 Spacelab Using Onboard GNSS Data." Sensors 18, no. 8 (August 14, 2018): 2671. http://dx.doi.org/10.3390/s18082671.
Testo completoAbstract (sommario):
Tiangong-2, the second Chinese manned spacecraft, was launched into low Earth orbit on 15 September 2016. The dual-frequency geodetic GNSS receiver equipped on it is supporting a number of scientific experiments in orbit. This paper uses the onboard GNSS data from 3–31 December 2016 (in the attitude mode of three-axis Earth-pointing stabilization) to analyze the data quantity, as well as the code multipath error. Then, the dynamic and reduced-dynamic methods are adopted to perform the post Precise Orbit Determination (POD) based on the carrier phase measurements, respectively. After that, the orbit accuracy is evaluated using a number of tests, which include the analysis of observation residuals, Overlapping Orbit Differences (OODs), orbit comparison between dynamic and reduced-dynamic and Satellite Laser Ranging (SLR) validation. The results show that: (1) the average Root Mean Square (RMS) of the on-board GNSS phase fitting residuals is 8.8 mm; (2) regarding the OODs determined by the reduced-dynamic method, the average RMS in radial (R), along-track (T) and cross-track (N) directions is 0.43 cm, 1.34 cm and 0.39 cm, respectively, and there are no obvious system errors; (3) the orbit accuracy of TG02 determined by the reduced-dynamic method is comparable to that of the dynamic method, and the average RMS of their differences in R, T, N and 3D directions is 3.05 cm, 3.60 cm, 2.52 cm and 5.40 cm, respectively; (4) SLR data are used to validate the reduced-dynamic orbits, and the average RMS along the station-satellite direction is 1.94 cm. It can be seen that both of these two methods can meet the demands of 3D centimeter-level orbit determination for TG02.
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Zheng, Yue, Binfeng Pan, Shuo Tang, and Yang Wang. "Multi-Step Control of Chaos in the Application of Earth-Moon Orbit Transfer." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 1 (February 2018): 35–41. http://dx.doi.org/10.1051/jnwpu/20183610035.
Testo completoAbstract (sommario):
A multi-step control of chaos method is proposed in this paper to reduce the flight time in the chaotic region of Earth-Moon low-energy orbit transfer. According to the motion regularity and the fact that the chaos orbit is highly sensitive to the initial conditions in the circular restricted three-body system, the optimal perturbation of chaos control at each step is calculated by the adaptive particle swarm optimization algorithm, and then the low-energy earth-moon orbit transfer trajectory is obtained. This proposed method can efficiently construct the Earth-Moon low-energy orbit transfer trajectory without the relying on the periodic orbits and the requirement of random search, and the corresponding flight time in chaotic motion can be significantly reduced. Finally, numerical simulations are provided to demonstrate the correctness and efficiency of this proposed method.
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Kazantsev, E. "Unstable periodic orbits and attractor of the barotropic ocean model." Nonlinear Processes in Geophysics 5, no. 4 (December 31, 1998): 193–208. http://dx.doi.org/10.5194/npg-5-193-1998.
Testo completoAbstract (sommario):
Abstract. A numerical method for detection of unstable periodic orbits on attractors of nonlinear models is proposed. The method requires similar techniques to data assimilation. This fact facilitates its implementation for geophysical models. This method was used to find numerically several low-period orbits for the barotropic ocean model in a square. Some numerical particularities of application of this method are discussed. Knowledge of periodic orbits of the model helps to explain some of these features like bimodality of probability density functions (PDF) of principal parameters. These PDFs have been reconstructed as weighted averages of periodic orbits with weights proportional to the period of the orbit and inversely proportional to the sum of positive Lyapunov exponents. The fraction of time spent in the vicinity of each periodic orbit has been compared with its instability characteristics. The relationship between these values shows the 93% correlation. The attractor dimension of the model has also been approximated as a weighted average of local attractor dimensions in vicinities of periodic orbits.
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Kwiecinski, James A., Stanisław W. Biber, and Robert A. Van Gorder. "Chaotic Rotations of a Rigid Ellipsoidal Body Exhibiting Spin-Orbit Misalignment in a Periodic Orbit." International Journal of Bifurcation and Chaos 29, no. 07 (June 30, 2019): 1930018. http://dx.doi.org/10.1142/s0218127419300180.
Testo completoAbstract (sommario):
We study chaotic rotations of a rigid ellipsoidal body due to the effects of gravitational torques, in the case where this body exhibits spin-orbit misalignment. After first deriving a simple model of a rigid ellipsoid of uniform mass distribution with principal axis of rotation directed slightly out of the orbital plane, we prove using the Melnikov method that this perturbation is sufficient to excite the ellipsoid to chaotically rotate for a circular orbit. We further verify this analytical result with numerical time series and Poincaré sections for circular orbits. We then use numerical simulations to demonstrate that elliptical orbits provide further pathways to chaos. Our primary finding is that increasing the degree of spin-orbit misalignment will increase the prevalence of initial conditions leading to chaotic dynamics, for elliptical bodies on both circular and elliptical orbits. Indeed, our results suggest that chaotic rotation of elongated bodies exhibiting spin-orbit misalignment is somewhat common for large enough deviation of the principal axis of rotation from the normal to the orbital plane, provided the rigid body lacks rotational symmetry around its spin-axis and, furthermore, exhibits sufficiently small angular momentum so that the effects of gravitational torques are nontrivial.
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Chebotarev, V. E., and E. O. Vorontsova. "Method of providing energy resources to a circumlunar satellite for passing longduration shadow zones." Spacecrafts & Technologies 4, no. 4 (December 4, 2020): 233–40. http://dx.doi.org/10.26732/j.st.2020.4.06.
Testo completoAbstract (sommario):
Researches of the possibilities of creating a lunar navigation and communication system have revealed features of the sun's illumination of near-lunar orbits: the annual passage of orbits through a long cycle of about 55 days, containing shadow sections of the orbit from the Moon and a pause of up to 185 days with possible overlays of penumbra and shadow sections of the orbit from the Earth. At the same time, the penumbra and shadow zones from the Earth near the Moon have significant differences in size and can cover the entire orbital grouping of the lunar navigation and communication system. As a result, the problem arises of calculating the energy resources of a circumlunar satellite for passing long-duration shadow zones and maintaining the spacecraft's thermal regime for the period of passing the shadow section of the orbit from the Earth. The energy balance of the spacecraft is modeled for various modes of its operation during the passage of long-duration shadow zones: regular, duty, storage. It is proposed to use blinds to regulate the heat radiation from the spacecraft radiators when passing the shadow sections of the orbit in the considered modes. To reduce the cost of spacecraft mass it is recommended to switch the spacecraft to storage mode, which reduces power consumption in comparison with standby mode. The efficiency of the proposed scheme for passing the shadow zones of the lunar navigation and communication system spacecraft was evaluated for three spacecraft sizes according to the criterion – the minimum amount of mass spent on increasing the energy intensity of the battery and installing blinds.
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Gao, Youtao, Tanran Zhao, Bingyu Jin, Junkang Chen, and Bo Xu. "Autonomous Orbit Determination for Lagrangian Navigation Satellite Based on Neural Network Based State Observer." International Journal of Aerospace Engineering 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/9734164.
Testo completoAbstract (sommario):
In order to improve the accuracy of the dynamical model used in the orbit determination of the Lagrangian navigation satellites, the nonlinear perturbations acting on Lagrangian navigation satellites are estimated by a neural network. A neural network based state observer is applied to autonomously determine the orbits of Lagrangian navigation satellites using only satellite-to-satellite range. This autonomous orbit determination method does not require linearizing the dynamical mode. There is no need to calculate the transition matrix. It is proved that three satellite-to-satellite ranges are needed using this method; therefore, the navigation constellation should include four Lagrangian navigation satellites at least. Four satellites orbiting on the collinear libration orbits are chosen to construct a constellation which is used to demonstrate the utility of this method. Simulation results illustrate that the stable error of autonomous orbit determination is about 10 m. The perturbation can be estimated by the neural network.
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Bakhtiari, Majid, Kamran Daneshjou, and Abbas Ali Mohammadi-Dehabadi. "The effects of parking orbit elements on designing of on-orbit servicing missions." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 3 (December 15, 2017): 793–810. http://dx.doi.org/10.1177/0954410017740921.
Testo completoAbstract (sommario):
Nowadays on-orbit servicing operations such as satellite refuelling, debris removal and visual inspection are considered as the most important issues in the space missions. Mission planning has a key role on the designation of such missions and it is strongly dependent on the required fuel. In this study, a new approach is proposed for the designing of the on-orbit operations with considering the parking orbit elements and location of the servicing satellites. The proposed method improves the previous mission planning process of the multiple servicing satellites in the terms of the reduction in the mission fuel consumption. Furthermore, a special rendezvous maneuver is considered for meeting the servicing satellites and the targets. Also, the transfer orbits are obtained through Lambert targeting. The optimisation of the problem is carried out by particle swarm optimisation algorithm and Taguchi technique is employed for the robust design of the control parameters of the optimisation algorithm. The results reveal that the proposed approach is an efficient way in the reduction of the fuel consumption in the on-orbit servicing missions rather than the conventional methods.
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Sui, Tao, Xiao Yu Zhang, Guang Shen Li, and Guan Nan Liu. "Research on Chaotic Orbit in Mandelbrot Set." Advanced Materials Research 912-914 (April 2014): 1349–52. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.1349.
Testo completoAbstract (sommario):
In this paper, the chaotic orbit in Mandelbrot set is introduced. On the basis of other scholars research, the character and distribution rules of pre-periodic orbits and pre-periodic points-Misiurewiz points about Mandelbrot set chaos-fractal images were studied. The software of constructing the general M-J set with Java Applet is improved. Using the method of computer mathematic experiments, the paper analyses the fixed orbit and period orbit in the M-set, gains the topology relationship of M set in super stable points, a recurrence formula between the period orbit and M-set periodic-buds is created.
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AVAN, JEAN, and ANTAL JEVICKI. "STRING FIELD ACTIONS FROM W∞." Modern Physics Letters A 07, no. 04 (February 10, 1992): 357–70. http://dx.doi.org/10.1142/s0217732392000306.
Testo completoAbstract (sommario):
Starting from W∞ as a fundamental symmetry and using the coadjoint orbit method, we derive an action for one-dimensional strings. It is shown that on the simplest non-trivial orbit this gives the single scalar collective field theory. On higher orbits one finds generalized KdV type field theories with increasing number of components.
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Wei, Zhang, Cui Wen, Wang Xiuhong, Wei Dong, and Liu Xing. "Re-entry prediction of objects with low-eccentricity orbits based on mean ballistic coefficients." Open Astronomy 29, no. 1 (November 22, 2020): 210–19. http://dx.doi.org/10.1515/astro-2020-0006.
Testo completoAbstract (sommario):
AbstractDuring re-entry objects with low-eccentricity orbits traverse a large portion of the dense atmospheric region almost every orbital revolution. Their perigee decays slowly, but the apogee decays rapidly. Because ballistic coefficients change with altitude, re-entry predictions of objects in low-eccentricity orbits are more difficult than objects in nearly circular orbits. Problems in orbit determination, such as large residuals and non-convergence, arise for this class of objects, especially in the case of sparse observations. In addition, it might be difficult to select suitable initial ballistic coefficient for re-entry prediction. We present a new re-entry prediction method based on mean ballistic coefficients for objects with low-eccentricity orbits. The mean ballistic coefficient reflects the average effect of atmospheric drag during one orbital revolution, and the coefficient is estimated using a semi-numerical method with a step size of one period. The method is tested using Iridium-52 which uses sparse observations as the data source, and ten other objects with low-eccentricity orbits which use TLEs as the data source. We also discuss the performance of the mean ballistic coefficient when used in the evolution of drag characteristics and orbit propagation. The results show that the mean ballistic coefficient is ideal for re-entry prediction and orbit propagation of objects with low-eccentricity orbits.
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Li, Shuangbao, Wensai Ma, Wei Zhang, and Yuxin Hao. "Melnikov Method for a Three-Zonal Planar Hybrid Piecewise-Smooth System and Application." International Journal of Bifurcation and Chaos 26, no. 01 (January 2016): 1650014. http://dx.doi.org/10.1142/s0218127416500140.
Testo completoAbstract (sommario):
In this paper, we extend the well-known Melnikov method for smooth systems to a class of planar hybrid piecewise-smooth systems, defined in three domains separated by two switching manifolds [Formula: see text] and [Formula: see text]. The dynamics in each domain is governed by a smooth system. When an orbit reaches the separation lines, then a reset map describing an impacting rule applies instantaneously before the orbit enters into another domain. We assume that the unperturbed system has a continuum of periodic orbits transversally crossing the separation lines. Then, we wish to study the persistence of the periodic orbits under an autonomous perturbation and the reset map. To achieve this objective, we first choose four appropriate switching sections and build a Poincaré map, after that, we present a displacement function and carry on the Taylor expansion of the displacement function to the first-order in the perturbation parameter [Formula: see text] near [Formula: see text]. We denote the first coefficient in the expansion as the first-order Melnikov function whose zeros provide us the persistence of periodic orbits under perturbation. Finally, we study periodic orbits of a concrete planar hybrid piecewise-smooth system by the obtained Melnikov function.
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Yavetz, Tomer D., Kathryn V. Johnston, Sarah Pearson, Adrian M. Price-Whelan, and Martin D. Weinberg. "Separatrix divergence of stellar streams in galactic potentials." Monthly Notices of the Royal Astronomical Society 501, no. 2 (November 28, 2020): 1791–802. http://dx.doi.org/10.1093/mnras/staa3687.
Testo completoAbstract (sommario):
ABSTRACT Flattened axisymmetric galactic potentials are known to host minor orbit families surrounding orbits with commensurable frequencies. The behaviour of orbits that belong to these orbit families is fundamentally different than that of typical orbits with non-commensurable frequencies. We investigate the evolution of stellar streams on orbits near the boundaries between orbit families (separatrices) in a flattened axisymmetric potential. We demonstrate that the separatrix divides these streams into two groups of stars that belong to two different orbit families, and that as a result, these streams diffuse more rapidly than streams that evolve elsewhere in the potential. We utilize Hamiltonian perturbation theory to estimate both the time-scale of this effect and the likelihood of a stream evolving close enough to a separatrix to be affected by it. We analyse two prior reports of stream-fanning in simulations with triaxial potentials, and conclude that at least one of them is caused by separatrix divergence. These results lay the foundation for a method of mapping the orbit families of galactic potentials using the morphology of stellar streams. Comparing these predictions with the currently known distribution of streams in the Milky Way presents a new way of constraining the shape of our Galaxy’s potential and distribution of dark matter.
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Sansaturio, M. Eugenia, Andrea Milani, and Luisa Cattaneo. "Nonlinear optimisation and the asteroid identification problem." Symposium - International Astronomical Union 172 (1996): 193–98. http://dx.doi.org/10.1017/s0074180900127342.
Testo completoAbstract (sommario):
Differential correction procedure allows us to improve orbits for which new observations are available; however, it only works provided the original orbit is within the convergence domain of the pseudo-Newton method. Given the strong nonlinearity of the problem, this only occurs when the residuals of the new observations with respect to the old orbit are quite small.
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Katsanikas, Matthaios, and Stephen Wiggins. "The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom – II." International Journal of Bifurcation and Chaos 31, no. 12 (September 25, 2021): 2150188. http://dx.doi.org/10.1142/s0218127421501881.
Testo completoAbstract (sommario):
We develop a method for the construction of a dividing surface using periodic orbits in Hamiltonian systems with three or more degrees-of-freedom that is an alternative to the method presented in [ Katsanikas & Wiggins, 2021 ]. Similar to that method, for an [Formula: see text] degrees-of-freedom Hamiltonian system, we extend a one-dimensional object (the periodic orbit) to a [Formula: see text] dimensional geometrical object in the energy surface of a [Formula: see text] dimensional space that has the desired properties for a dividing surface. The advantage of this new method is that it avoids the computation of the normally hyperbolic invariant manifold (NHIM) (as the first method did) and it is easier to numerically implement than the first method of constructing periodic orbit dividing surfaces. Moreover, this method has less strict required conditions than the first method for constructing periodic orbit dividing surfaces. We apply the new method to a benchmark example of a Hamiltonian system with three degrees-of-freedom for which we are able to investigate the structure of the dividing surface in detail. We also compare the periodic orbit dividing surfaces constructed in this way with the dividing surfaces that are constructed starting with a NHIM. We show that these periodic orbit dividing surfaces are subsets of the dividing surfaces that are constructed from the NHIM.
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Yao, Peter, and Timothy Sands. "Micro Satellite Orbital Boost by Electrodynamic Tethers." Micromachines 12, no. 8 (July 31, 2021): 916. http://dx.doi.org/10.3390/mi12080916.
Testo completoAbstract (sommario):
In this manuscript, a method for maneuvering a spacecraft using electrically charged tethers is explored. The spacecraft’s velocity vector can be modified by interacting with Earth’s magnetic field. Through this method, a spacecraft can maintain an orbit indefinitely by reboosting without the constraint of limited propellant. The spacecraft-tether system dynamics in low Earth orbit are simulated to evaluate the effects of Lorentz force and torques on translational motion. With 500-meter tethers charged with a 1-amp current, a 100-kg spacecraft can gain 250 m of altitude in one orbit. By evaluating the combined effects of Lorenz force and the coupled effects of Lorentz torque propagation through Euler’s moment equation and Newton’s translational motion equations, the simulated spacecraft-tether system can orbit indefinitely at altitudes as low as 275 km. Through a rare evaluation of the nonlinear coupling of the six differential equations of motion, the one finding is that an electrodynamic tether can be used to maintain a spacecraft’s orbit height indefinitely for very low Earth orbits. However, the reboost maneuver is inefficient for high inclination orbits and has high electrical power requirement. To overcome greater aerodynamic drag at lower altitudes, longer tethers with higher power draw are required.
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Oliveira, Thais C., and Antonio F. B. A. Prado. "SEARCH FOR STABLE ORBITS AROUND THE BINARY ASTEROID SYSTEMS 1999 KW4 AND DIDYMOS." Revista Mexicana de Astronomía y Astrofísica 56, no. 1 (April 1, 2020): 113–28. http://dx.doi.org/10.22201/ia.01851101p.2020.56.01.12.
Testo completoAbstract (sommario):
This work includes analytical and numerical studies of spacecrafts orbiting two binary asteroid systems: 1999 KW4 and Didymos. The binary systems are modeled as full irregular bodies, such that the whole evolution of the results will show the impact of the irregular gravity field in the lifetime and dynamics of the spacecraft’s orbit. The equations of motion of the binary system and the spacecraft are derived from Lagrange Equations. The solar radiation pressure is consired in the dynamics of the spacecraft.Two distinct methods are used to search for stable orbits around the binary systems. One is called the grid search method, which defines the main body as a point mass to estimate the initial state of the spacecraft based on a circular Keplerian orbit. The second method is the search for periodic orbits based on zero-velocity surfaces.
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Fu, Shihui. "Existence of Impact Period-1 Orbit After Grazing Bifurcation for a Soft Impacting System." International Journal of Bifurcation and Chaos 31, no. 07 (June 15, 2021): 2150103. http://dx.doi.org/10.1142/s0218127421501030.
Testo completoAbstract (sommario):
In the paper, the theoretical study on some experimental and numerical results of grazing bifurcation for a soft impacting system are analyzed. After the conditions under which nonimpact period-1 orbit and grazing bifurcation exist are given, we prove that an impact period-1 orbit exists by the implicit function theorem. The details of these periodic orbits are also investigated, which also helps us numerically find them. The method in this paper is still efficient for the multiperiodic orbits with single impact.