scholarly journals Determination of Eccentric Anomaly for Kepler’s Satellite Orbit Using Perturbation-Based Seeded Secant Iteration Scheme

Author(s):  
Dike H.U. ◽  
Isaac A.E.

In this paper, the determination of eccentric anomaly (E) for Kepler’s satellite orbit using Perturbation-Based Seeded Secant (PBSS) iteration algorithm is presented. The solution is meant for Kepler’s orbit with the value of eccentricity (e) in the range 0 ≤ e ≤ 1. Such orbits are either circular or elliptical. The demonstration of the applicability of the PBSS iteration is presented using sample numerical examples with different values of mean anomaly (M) and eccentricity (e). The summary of the results of E for M = 30° and e in the range 0.001 ≤ e ≤1 showed that the convergence cycle (n) increases as e increases. Particularly, n increased from 2 at e = 0.01 to n = 8 at e =1. The implication is that it takes more iterations to arrive at the value of E with the desired accuracy or error performance (which in this case is set to 10^(-12)). Another implication is that a good choice of the initial value of E is essential especially as the value of e increases. As such, effort should be made to develop a means of estimating the initial value of E which will reduce the convergence cycle for higher values of e.

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.


2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.


2006 ◽  
Vol 129 (6) ◽  
pp. 649-652 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-P̱RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach.


2020 ◽  
Vol 4 (3) ◽  
pp. 313-322
Author(s):  
Sunday Obomeviekome Imoni ◽  
D. I. Lanlege ◽  
E. M. Atteh ◽  
J. O. Ogbondeminu

ABSTRACT In this paper, formulation of an efficient numerical schemes for the approximation first-order initial value problems (IVPs) of ordinary differential equations (ODE) is presented. The method is a block scheme for some k-step linear multi-step methods (and) using the Hermite Polynomials a basis function. The continuous and discrete linear multi-step methods (LMM) are formulated through the technique of collocation and interpolation. Numerical examples of ODE have been examined and results obtained show that the proposed scheme can be efficient in solving initial value problems of first order ODE.


2013 ◽  
Vol 353-356 ◽  
pp. 3456-3459 ◽  
Author(s):  
Qiao Li Kong ◽  
Jin Yun Guo ◽  
Li Tao Han

DORIS is a kind of advanced space-geodetic techniques applied in satellite orbit tracking and measuring. As the first ocean dynamic environmental satellite in China, the HY-2 satellite is equipped with the Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking system for the precise orbit determination. In particular, the investigation of our work has focused on accuracy analysis of orbit determination using simulated DORIS data given different observation noises, besides the relationship is investigated between accuracy and computation time and the number of ground beacons evenly distributed around the world. Experiment results show that observation noises can affect the accuracy of orbit determination directly, and the number of DORIS ground beacons decides the accuracy and computation time of obit determination in the condition of ground beacons are evenly distributed around the world, therefore, during the process of obit determination, we should optimize the ground beacon station distribution to achieve the best accuracy of obit determination using DORIS tracking data.


2015 ◽  
Vol 5 (4) ◽  
pp. 301-311 ◽  
Author(s):  
Lijun Yi

AbstractThe h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.


2020 ◽  
Vol 635 ◽  
pp. A23 ◽  
Author(s):  
D. Futyan ◽  
A. Fortier ◽  
M. Beck ◽  
D. Ehrenreich ◽  
A. Bekkelien ◽  
...  

Context. The CHaracterising ExOPlanet Satellite (CHEOPS) is a mission dedicated to the search for exoplanetary transits through high precision photometry of bright stars already known to host planets. The telescope will provide the unique capability of determining accurate radii for planets whose masses have already been measured from ground-based spectroscopic surveys. This will allow a first-order characterisation of the planets’ internal structure through the determination of the bulk density, providing direct insight into their composition. By identifying transiting exoplanets with high potential for in-depth characterisation, CHEOPS will also provide prime targets for future instruments suited to the spectroscopic characterisation of exoplanetary atmospheres. Aims. The CHEOPS simulator has been developed to perform detailed simulations of the data which is to be received from the CHEOPS satellite. It generates accurately simulated images that can be used to explore design options and to test the on-ground data processing, in particular, the pipeline producing the photometric time series. It is, thus, a critical tool for estimating the photometric performance expected in flight and to guide photometric analysis. It can be used to prepare observations, consolidate the noise budget, and asses the performance of CHEOPS in realistic astrophysical fields that are difficult to reproduce in the laboratory. Methods. The simulator has been implemented as a highly configurable tool called CHEOPSim, with a web-based user interface. Images generated by CHEOPSim take account of many detailed effects, including variations of the incident signal flux and backgrounds, and detailed modelling of the satellite orbit, pointing jitter and telescope optics, as well as the CCD response, noise and readout. Results. The simulator results presented in this paper have been used in the context of validating the data reduction processing chain, in which image time series generated by CHEOPSim were used to generate light curves for simulated planetary transits across real and simulated targets. Independent analysts were successfully able to detect the planets and measure their radii to an accuracy within the science requirements of the mission: for an Earth-sized planet with an orbital period of 50 days orbiting a Sun-like target with magnitude V = 6, the median measured value of the planet to star radius ratio, Rp/Rs, was 0.00923 ± 0.00054(stat) ± 0.00019(syst), compared to a true input value of 0.00916. For a Neptune-sized planet with an orbital period of 13 days orbiting a target with spectral type K5V and magnitude V = 12, the median measured value of Rp/Rs was 0.05038 ± 0.00061(stat) ± 0.00031(syst), compared to a true input value of 0.05.


1979 ◽  
Vol 23 ◽  
pp. 133-141
Author(s):  
C. A. Seils ◽  
G. T. Tisue

A recent surge of interest in sulfur in the environment has revealed the need for improved methods of analysis for sulfate, SO4=, in rain, freshwater and sediment interstitial fluids. Ion chromatography permits the rapid determination of SO4= in the ppm range (1 ppm = 1 mgL'1 = 10 μmol L-1 sulfate) on relatively small samples with good specificity. If a suitable instrument is available, this technique is a good choice for many environmental analyses. Other approaches to sulfate analysis are based on its precipitation with organic or heavy metal cations, usually barium or lead. The amount of precipitate formed may be determined by inter alia gravimetry, turbidimetry, radiometry (using 133-Ba), atomic absorption spectrophotometry (Ba or Pb detection), potentiometry (using a Pb++ ion selective electrode) , colorimetry, or by x-ray fluorescence spectrometry (Ba, Pb or S detection)(1). Because of our experience with x-ray fluorescence analyses, we chose to develop and test a procedure using that technique.


Author(s):  
Krishnan Suresh

In multi-objective topology optimization, a design is defined to be “pareto-optimal” if no other design exists that is better with respect to one objective, and as good with respect to others. This unfortunately suggests that unless other ‘better’ designs are found, one cannot declare a particular topology to be pareto-optimal. In this paper, we first show that a topology can be guaranteed to be (locally) pareto-optimal if certain inherent properties associated with the topological sensitivity field are satisfied, i.e., no further comparison is necessary. This, in turn, leads to a deterministic, i.e., non-stochastic, method for directly tracing pareto-optimal frontiers using the classic fixed-point iteration scheme. The proposed method can generate the full set of pareto-optimal topologies in a single-run, and is therefore both efficient and predictable, as illustrated through numerical examples.


Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xianming Wu ◽  
Weijie Tan ◽  
Huihai Wang

In this paper, a method for determining the initial value of the hidden attractors in the Chua system is studied. The initial value of the hidden attractors can be calculated quickly and accurately by the proposed method, and the hidden attractors can be found by numerical simulation. Then, the initial values of the hidden attractors are set accurately by digital signal processor (DSP), so as to the circuit realization of the chaotic system with hidden attractors is performed. The results show that the numerical simulation results of Matlab are consistent with the experimental results of DSP.


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