Hamiltonian Perturbation Solutions for Spacecraft Orbit Prediction

2021 ◽  
Author(s):  
Martín Lara
2014 ◽  
Vol 59 (7) ◽  
pp. 321-325 ◽  
Author(s):  
Yu. G. Markov ◽  
M. V. Mikhailov ◽  
V. N. Pochukaev

2021 ◽  
Author(s):  
Shunchenqiao Bai ◽  
Guangwei Wen ◽  
Zhaokui Wang

Abstract Atmospheric drag calculation error greatly reduce the low-earth orbit spacecraft trajectory prediction fidelity. To solve the issue, the "correction - prediction" strategy is usually employed. In the method, one parameter is fixed and other parameters are revised by inverting spacecraft orbit data. However, based on a single spacecraft data, the strategy usually performs poorly as parameters in drag force calculation are coupled with each other, which result in convoluted errors. A gravity field recovery and atmospheric density detection satellite, Q-Sat, developed by xxxxx Lab at xxx University, is launched on August 6th, 2020. The satellite is designed to be spherical for a constant drag coefficient regardless of its attitude. An orbit prediction method for low-earth orbit spacecraft with employment of Q-Sat data is proposed in present paper for decoupling atmospheric density and drag coefficient identification process. For the first step, by using a dynamic approach-based inversion, several empirical atmospheric density models are revised based on Q-Sat orbit data. Depends on the performs, one of the revised atmospheric density model would be selected for the next step in which the same inversion is employed for drag coefficient identification for a low-earth orbit operating spacecraft whose orbit needs to be predicted. Finally, orbit forecast is conducted by extrapolation with the dynamic parameters in the previous steps. Tests are carried out for the proposed method by using a GOCE satellite 15-day continuous orbit data. Compared with legacy “correction - prediction” method in which only GOCE data is employed, the accuracy of the 24-hour orbit prediction is improved by about 171m the highest for the proposed method. 14-day averaged 24-hour prediction precision is elevated by approximately 70m.


Author(s):  
Amarjot Singh Bhullar ◽  
Gospel Ezekiel Stewart ◽  
Robert W. Zimmerman

Abstract Most analyses of fluid flow in porous media are conducted under the assumption that the permeability is constant. In some “stress-sensitive” rock formations, however, the variation of permeability with pore fluid pressure is sufficiently large that it needs to be accounted for in the analysis. Accounting for the variation of permeability with pore pressure renders the pressure diffusion equation nonlinear and not amenable to exact analytical solutions. In this paper, the regular perturbation approach is used to develop an approximate solution to the problem of flow to a linear constant-pressure boundary, in a formation whose permeability varies exponentially with pore pressure. The perturbation parameter αD is defined to be the natural logarithm of the ratio of the initial permeability to the permeability at the outflow boundary. The zeroth-order and first-order perturbation solutions are computed, from which the flux at the outflow boundary is found. An effective permeability is then determined such that, when inserted into the analytical solution for the mathematically linear problem, it yields a flux that is exact to at least first order in αD. When compared to numerical solutions of the problem, the result has 5% accuracy out to values of αD of about 2—a much larger range of accuracy than is usually achieved in similar problems. Finally, an explanation is given of why the change of variables proposed by Kikani and Pedrosa, which leads to highly accurate zeroth-order perturbation solutions in radial flow problems, does not yield an accurate result for one-dimensional flow. Article Highlights Approximate solution for flow to a constant-pressure boundary in a porous medium whose permeability varies exponentially with pressure. The predicted flowrate is accurate to within 5% for a wide range of permeability variations. If permeability at boundary is 30% less than initial permeability, flowrate will be 10% less than predicted by constant-permeability model.


Author(s):  
Adam W. Koenig ◽  
Simone D'Amico ◽  
Eliad Peretz ◽  
Wayne Yu ◽  
Sun Hur-Diaz ◽  
...  

1994 ◽  
Vol 31 (3) ◽  
pp. 447-452 ◽  
Author(s):  
Michele M. Gates ◽  
Mark J. Lewis

2021 ◽  
Vol 14 (5) ◽  
pp. 285
Author(s):  
Tamer Mekky Habib ◽  
Reham Abdellatif Abouhogail

Author(s):  
Feras K. Alfosail ◽  
Amal Z. Hajjaj ◽  
Mohammad I. Younis

We investigate theoretically and experimentally the two-to-one internal resonance in micromachined arch beams, which are electrothermally tuned and electrostatically driven. By applying an electrothermal voltage across the arch, the ratio between its first two symmetric modes is tuned to two. We model the nonlinear response of the arch beam during the two-to-one internal resonance using the multiple scales perturbation method. The perturbation solution is expanded up to three orders considering the influence of the quadratic nonlinearities, cubic nonlinearities, and the two simultaneous excitations at higher AC voltages. The perturbation solutions are compared to those obtained from a multimode Galerkin procedure and to experimental data based on deliberately fabricated Silicon arch beam. Good agreement is found among the results. Results indicate that the system exhibits different types of bifurcations, such as saddle node and Hopf bifurcations, which can lead to quasi-periodic and potentially chaotic motions.


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