Expansion of the third-body disturbing function

1980 ◽  
Author(s):  
R. BROUCKE
Keyword(s):  
Disturbing Function ◽  
Third Body ◽  
The Third

scholarly journals Integrable Cases of Satellite Problem with the Third Body and the Oblate Planet

1974 ◽  
Vol 62 ◽  
pp. 117-124
Author(s):  
M. L. Lidov
Keyword(s):  
Elliptic Orbit ◽  
Disturbing Function ◽  
Third Body ◽  
The Third ◽  
Satellite Problem ◽  
Oblate Planet

The evolutions of satellite's orbit under the influence of the third disturbing body moving on an elliptic orbit and the oblate planet are studied by averaging the disturbing function, and integrable cases are classified in seven cases.

scholarly journals Expansion of the Disturbing Function by Factorization

1981 ◽  
Vol 63 ◽  
pp. 337-348
Author(s):  
R. Broucke ◽  
W. Presler
Keyword(s):  
Magnetic Tape ◽  
Disturbing Function ◽  
Third Body ◽  
The Third ◽  
Five Elements

AbstractWe present an expansion of the disturbing function for the third-body perturbations in the form , where ε is the ratio of semi-major axes (a/a’) and Xnm and Ynm depend only on the five elements e, i, ω, Ω, of the satellite while and depend on the corresponding elements of the perturbing body. Each one of the four functions X and Y is represented as a product of two factors as opposed to three factors in our previous publication of this subject (Broucke, 1981). We develop several relations for the construction of the X and Y-series. These series are relatively short and can be computed in advance and stored on magnetic tape, for instance.

scholarly journals Orbital Design and Control for Jupiter-Observation Spacecraft

Aerospace ◽  
2021 ◽  
Vol 8 (10) ◽  
pp. 282
Author(s):  
Chunsheng Jiang ◽  
Yongjie Liu ◽  
Yu Jiang ◽  
Hengnian Li
Keyword(s):  
Local Time ◽  
Semimajor Axis ◽  
Disturbing Function ◽  
Atmospheric Drag ◽  
Third Body ◽  
Dynamical Models ◽  
Ground Track ◽  
The Third ◽  
Reasonable Range ◽  
And Control

This paper investigates the evolution of orbits around Jupiter and designs a sun-synchronous repeating ground track orbit. In the dynamical models, the leading terms of the Jupiter’s oblateness are J2 and J4 terms. A reasonable range of ground track repetition parameter Q is given and the best observation orbit elements are selected. Meanwhile, the disturbing function acting on the navigation spacecraft is the atmospheric drag and the third body. The law of altitude decay of the spacecraft’s semimajor orbit axis caused by the atmospheric drag is studied, and the inclination perturbation caused by the sun’s gravity is analyzed. This paper designs a semimajor axis compensation strategy to maintain the orbit’s repeatability and proposes an initial inclination prebiased strategy to limit the local time at the descending node in a permitted range. In particular, these two methods are combined in the context of sun-synchronous repeating ground track orbit for better observation of the surface of Jupiter.

scholarly journals Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

2021 ◽  
Vol 133 (3) ◽  
Author(s):  
Marilena Di Carlo ◽  
Simão da Graça Marto ◽  
Massimiliano Vasile
Keyword(s):  
Gravitational Perturbation ◽  
Low Thrust ◽  
Orbital Elements ◽  
Third Body ◽  
The Third ◽  
Orbital Perturbations ◽  
Analytical Formulae ◽  
Numerical Orbit ◽  
Body Potential

AbstractThis paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

The Effect of the Third Body on the Fretting Wear Behavior of Coatings

2002 ◽  
Vol 11 (3) ◽  
pp. 288-293 ◽  
Author(s):  
Gui-Zhen Xu ◽  
Jia-Jun Liu ◽  
Zhong-Rong Zhou
Keyword(s):  
Wear Behavior ◽  
Fretting Wear ◽  
Third Body ◽  
The Third

A mathematical model for the third-body concept

2017 ◽  
Vol 23 (3) ◽  
pp. 420-432 ◽  
Author(s):  
Pavel Krejčí ◽  
Adrien Petrov
Keyword(s):  
Mathematical Model ◽  
A Priori Estimates ◽  
A Priori ◽  
Dynamical Problem ◽  
Sobolev Embedding ◽  
Third Body ◽  
Embedding Theory ◽  
The Third ◽  
Galerkin Approximations ◽  
Body Concept

The third-body concept is a pragmatic tool used to understand the friction and wear of sliding materials. The wear particles play a crucial role in this approach and constitute the main part of the third-body. This paper aims to introduce a mathematical model for the motion of a third-body interface separating two surfaces in contact. This model is written in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this dynamical problem is obtained by using a priori estimates established for Faedo–Galerkin approximations, and some more specific techniques such as anisotropic Sobolev embedding theory.

scholarly journals A preservação de acervos históricos no estado de Minas Gerais: Projeto Memorial da Imprensa de Uberaba – criação da Hemeroteca Digital do Triângulo Mineiro e Alto Paranaíba (The preservation of historical...)

2015 ◽  
Vol 16 (25) ◽  
pp. 168
Author(s):  
Vilma Moreira dos Santos ◽  
Thiago Veloso Vitral ◽  
Alessandra Palhares
Keyword(s):  
Digital Library ◽  
Digital Libraries ◽  
Minas Gerais ◽  
Printing Press ◽  
Third Body ◽  
Main Achievement ◽  
Historical Collections ◽  
The Third ◽  
The Creation ◽  
Anglo American

<p>O Projeto <strong>Memorial da Imprensa de Uberaba: criação da Hemeroteca Digital do Triângulo Mineiro e Alto Paranaíba </strong>constitui, provavelmente, o maior investimento do estado de Minas Gerais em um projeto individual na área de preservação de acervos documentais históricos. O projeto conta com o financiamento da Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG). Foi concebido e vem sendo executado por parceria firmada entre a Secretaria de Estado de Ciência, Tecnologia e Ensino Superior (SECTES/MG) e a Secretaria de Estado de Cultura (SEC/MG), por meio do Arquivo Público Mineiro (APM), órgão coordenador do Projeto e da Superintendência de Bibliotecas Públicas (SUB). Conta ainda com a participação do Arquivo Público de Uberaba. A partir das diretrizes de regionalização da política cultural do Estado, o resultado principal do projeto será a implantação de um polo de digitalização de acervos documentais históricos no Arquivo Público de Uberaba, que deverá atuar como órgão catalizador e executor de projetos de digitalização nas regiões acima mencionadas. O projeto se fundamenta nas metodologias de organização, preservação e digitalização de acervos documentais preconizadas pelo <strong>Programa Conservação Preventiva em Bibliotecas e Arquivos</strong>, nas recomendações do Conselho Nacional de Arquivos (CONARQ) e nas regras do Código de Catalogação Anglo-americano (CCAA2).</p><p><strong><br /></strong></p><p><strong>Abstract</strong></p><p>“The Printing Press Memorial of Uberaba: the creation of the newspapers´ digital library of Triângulo Mineiro and Alto Paranaíba (Minas Gerais, Brazil)” is probably, the biggest project in the field of historical collections preservation ever funded by the Fundação de Amparo à Pesquisa do Estado de Minas Gerais – FAPEMIG. The project was conceived and has been carried out by the Secretaria de Estado de Ciência, Tecnologia e Ensino Superior, along with the Secretaria de Estado de Cultura, through the participation of the Arquivo Público Mineiro, the coordinating body, and the Superintendência de Bibliotecas Públicas. The<em> </em>Arquivo Público de Uberaba is the third body involved with the implementation of the project. In accordance with the regionalization policies of the State, the main achievement of the project shall be the creation of a digitalization center of historical collections in the Arquivo Público de Uberaba. This institution shall act as a regional agency for the development of digitalization projects in the regions of Triângulo Mineiro and Alto Paranaíba. The project is based on the methodologies of organization, preservation and digitalization of historical collections, recommended by the Programa de Conservação Preventiva em Bibliotecas e Arquivos, the guidelines of the Conselho Nacional de Arquivos<em> </em>(CONARQ) and the Anglo American Cataloguing Rules (AACR2).</p><p><strong>Keywords</strong>: Digitalization of Historical collections; Preservation of Historical Collections; Digital Libraries.</p>

scholarly journals γ DOR: A PULSATING COMPONENT OF KIC 8043961 IN A STELLAR TRIPLE SYSTEM

2020 ◽  
Vol 56 (2) ◽  
pp. 179-191
Author(s):  
C. Kamil ◽  
H. A. Dal ◽  
O. Özdarcan ◽  
E. Yoldaş
Keyword(s):  
Major Axis ◽  
Primary Component ◽  
Mass Ratio ◽  
Third Body ◽  
Semi Major Axis ◽  
Orbital Inclination ◽  
The Third ◽  
New Findings ◽  
Effective Temperatures ◽  
Orbit Model

We present new findings about KIC 8043961. We find the effective temperatures of the components as 6900 ± 200 K for the primary, and 6598 ± 200 K for the secondary, while the logarithm of the surface gravities are found to be 4.06 cm s-2 and 3.77 cm s-2, respectively. Combination of the light curve with the spectroscopic orbit model results leads to a mass ratio of 1.09 ± 0.07 with an orbital inclination of 73.71 ± 0.14 and a semi-major axis of 8.05 ± 0.22 R⨀ . Masses of the primary and secondary components are calculated as 1.379 ± 0.109 M⨀ and 1.513 ± 0.181 M⨀, while the radii are found to be 1.806 ± 0.084 R⨀ and 2.611 ± 0.059 R⨀. In addition, we obtain a considerable light contribution (≈0.54%) of a third body. We compute a possible mass for the third body as 0.778 ± 0.002 M⨀. We find that the primary component exhibits γ Dor type pulsations with 137 frequencies.

Fretting Wear Mechanisms and Their Effects on Fretting Fatigue

1988 ◽  
Vol 110 (3) ◽  
pp. 517-524 ◽  
Author(s):  
Y. Berthier ◽  
Ch. Colombie´ ◽  
L. Vincent ◽  
M. Godet
Keyword(s):  
Fretting Fatigue ◽  
Relative Displacement ◽  
Contact Condition ◽  
Fretting Wear ◽  
Initial Contact ◽  
Great Care ◽  
Third Body ◽  
Body Formation ◽  
The Third ◽  
Contact Surfaces

Fretting wear and fretting fatigue are governed by the rate of formation of materials (third-bodies) between the initial contact surfaces. Furthermore, the third-bodies must be maintained within the contact. The issue of the race between third-body formation and subsurface damage conditions the effect of fretting on fatigue. That race lasts for only a few hundred or at best a few thousand cycles. Effective third-bodies (or good anti-fretting lubricants) must adhere strongly to the rubbing surfaces, and be able to accommodate at least part of the relative displacement. Great care in the design of test equipment has to be exercised before definitive results on the effect of amplitude and frequency on either fretting fatigue or fretting wear can be obtained for a given contact condition, given materials and given environments.

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