F and G Taylor series solutions to the Stark and Kepler problems with Sundman transformations

Pellegrini, Etienne; Russell, Ryan P.; Vittaldev, Vivek

doi:10.1007/s10569-014-9538-7

Cited by 14 publications

(12 citation statements)

References 33 publications

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“…Another analytical study proposed by Biscani and Izzo (2014) uses the Weierstrassian formulations to solve the motions for bounded and unbounded trajectories and to find periodic motions. Also, the motion can be approached numerically by developing the equations of motion in Taylor series but this leads to some issues for high eccentricities (Pellegrini et al, 2014). Hatten and Russell (2014) compared recently these methods and their computing efficiencies.…”

Section: Introductionmentioning

confidence: 99%

Theory for planetary exospheres: I. Radiation pressure effect on dynamical trajectories

Beth

Garnier

Toublanc

et al. 2016

Icarus

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The planetary exospheres are poorly known in their outer parts, since the neutral densities are low compared with the instruments detection capabilities. The exospheric models are thus often the main source of information at such high altitudes. We present a new way to take into account analytically the additional effect of the radiation pressure on planetary exospheres. In a series of papers, we present with an Hamiltonian approach the effect of the radiation pressure on dynamical trajectories, density profiles and escaping thermal flux. Our work is a generalization of the study by Bishop and Chamberlain (1989). In this first paper, we present the complete exact solutions of particles trajectories, which are not conics, under the influence of the solar radiation pressure. This problem was recently partly solved by Lantoine and Russell (2011) and completely by Biscani and Izzo (2014). We give here the full set of solutions, including solutions not previously derived, as well as simpler formulations for previously known cases and comparisons with recent works. The solutions given may also be applied to the classical Stark problem (Stark, 1914): we thus provide here for the first time the complete set of solutions for this well-known effect in term of Jacobi elliptic functions.

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Section: Introductionmentioning

confidence: 99%

Theory for planetary exospheres: I. Radiation pressure effect on dynamical trajectories

Beth

Garnier

Toublanc

et al. 2016

Icarus

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“…Как в случае импульсного управле-ния, так и в случае управления ускорением тяги, уравнения движения инте-грируются численно методом Рунге-Кутты 8-го порядка с постоянным ша-гом. Отметим, что в случае управления ускорением тяги возникающие зада-чи Коши можно решать и полуаналитическими методами, наиболее эффек-тивным с точки зрения быстродействия и простым в реализации из которых, как показали исследования Р. Рассела [17], оказался метод Пеллегрини [16]. В разделе 6 приводятся некоторые результаты расчетов этим методом.…”

Section: результаты расчетовunclassified

“…Метод был реализован на языке програм-мирования Fortran 90 с использованием компилятора Intel Fortran и оптими-зационного пакета SNOPT 7.6 [23]. При интегрировании уравнений движе-ния использовалась реализация метода Пеллегрини решения задачи Штарка, предложенная в работе [16].…”

Section: расчеты на вычислительном кластереunclassified

“…Эта задача называется задачей Штарка [13] и может быть решена как с помощью численного интегрирова-ния, так и аналитически. Основными современными и эффективными ана-литическими методами решения задачи Штарка являются методы, разрабо-танные Г. Лантуаном [14], Ф. Бискани [15] и Э. Пеллегрини [16]. Согласно исследованиям, проведенным Р. Расселом [17], использование аналитических методов помогает повысить быстродействие и точность вычислений.…”

Section: Introductionunclassified

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Comparison of two direct interplanetary trajectory optimization techniques

Tselousova¹,

Shirobokov

Trofimov

2018

KIAM Prepr.

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“…One of the most commonly used single-step methods for performing high-fidelity integration is the high-order Runge-Kutta technique [36,40]. Other techniques have recently shown promise, including the collocation methods [34], the Taylor series integration methods [41,42], and Picard iteration techniques [43]. The explicit Runge-Kutta (RK) integration technique is chosen for this work due to its widespread use, customization, and ease of implementation [44] [particularly in the context of graphics processing unit (GPU) programming].…”

Section: Introductionmentioning

confidence: 99%

Parallel Computation of Trajectories Using Graphics Processing Units and Interpolated Gravity Models

Arora

Vittaldev

Russell

2015

Journal of Guidance, Control, and Dynamics

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Seeking improvements in speed and accuracy in multiobject trajectory simulations, a solution methodology is presented that takes advantage of 1) new high-fidelity geopotential and third-body perturbation models that efficiently trade memory for speed, and 2) a graphics processing unit based integrator to achieve parallelism across multiple objects. The two methods combined lead to multiplicative speedups, making the tool three orders of magnitude faster, in some cases, compared to the same simulation performed in serial on a single central processing unit. The tool is capable of Monte Carlo simulations of a single object or of propagating the mean and covariance of all the objects in a space catalog. The tool performance is demonstrated for 1) a five-day Monte Carlo simulation of the state uncertainty point cloud modeled with over one million objects, and 2) a seven-day simulation of position and velocity states of a full space catalog with over 250,000 objects. The simulations required approximately 1 and 3 h of runtime, respectively, on a single desktop workstation using a single-core central processing unit and a single graphics processing unit. The solution method is applicable to a variety of space situational awareness applications, including orbit determination, catalog maintenance, uncertainty propagation, and conjunction analysis.

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F and G Taylor series solutions to the Stark and Kepler problems with Sundman transformations

Cited by 14 publications

References 33 publications

Theory for planetary exospheres: I. Radiation pressure effect on dynamical trajectories

Theory for planetary exospheres: I. Radiation pressure effect on dynamical trajectories

Comparison of two direct interplanetary trajectory optimization techniques

Parallel Computation of Trajectories Using Graphics Processing Units and Interpolated Gravity Models

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