Relevant bibliographies by topics / Circular Restricted Three Body Problem

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Circular Restricted Three Body Problem'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Circular Restricted Three Body Problem.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Circular Restricted Three Body Problem"

1

Dionysiou, D. D., and D. A. Vaiopoulos. "On the restricted circular three-charged-body problem." Astrophysics and Space Science 135, no. 2 (1987): 253–60. http://dx.doi.org/10.1007/bf00641560.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Vrbik, Jan. "Chaos in Planar, Circular, Restricted Three-Body Problem." Applied Mathematics 04, no. 01 (2013): 40–45. http://dx.doi.org/10.4236/am.2013.41008.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Minglibayev, M. Zh, and T. M. Zhumabek. "ON THE RESTRICTED THREE-BODY PROBLEM." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (April 15, 2021): 138–44. http://dx.doi.org/10.32014/2021.2518-1726.33.

Full text
Abstract:
The paper analytically investigates the classical restricted three-body problem in a special non-inertial central coordinate system, with the origin at center of forces. In this coordinate system, an analytical expression of the invariant of the centre of forces is given. The existence of the invariant of the centre of forces admits the correct division of the problem into two problems. The first is a triangular restricted three-body problem. The second is a collinear restricted three-body problem. In this paper the collinear restricted three-body problem is investigated. Using the properties of the invariant of centre of forces of the restricted three-body problem in the special non- inertial central coordinate system, the basic differential equations of motion for the collinear restricted three-body problem are obtained when three bodies lie on the same line during all motion. Differential equations of the collinear restricted three-body problem in the rotating non-inertial central coordinate system in pulsating variables are derived. New differential equations of motion for the collinear restricted three-body problem in three regions of possible location of the massless body with stationary solutions corresponding to the three Euler libration points have been derived. The circular collinear restricted three-body problem is investigated in detail. The corresponding Jacobi integrals are obtained. New exact non-stationary partial analytical solutions of the obtained new differential equations of motion of the collinear restricted three-body problem have been found for the considered case.
APA, Harvard, Vancouver, ISO, and other styles
4

Campagnola, Stefano, Paul Skerritt, and Ryan P. Russell. "Flybys in the planar, circular, restricted, three-body problem." Celestial Mechanics and Dynamical Astronomy 113, no. 3 (June 22, 2012): 343–68. http://dx.doi.org/10.1007/s10569-012-9427-x.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Rodica, Roman, and Mioc Vasile. "Libration Points in Schwarzschild's Circular Restricted Three-Body Problem." Astrophysics and Space Science 304, no. 1-4 (July 19, 2006): 101–3. http://dx.doi.org/10.1007/s10509-006-9083-2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Guzzetti, Davide, and Kathleen Connor Howell. "Attitude dynamics in the circular restricted three-body problem." Astrodynamics 2, no. 2 (May 15, 2018): 87–119. http://dx.doi.org/10.1007/s42064-017-0012-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Palacián, J. F., C. Vidal, J. Vidarte, and P. Yanguas. "Dynamics in the Charged Restricted Circular Three-Body Problem." Journal of Dynamics and Differential Equations 30, no. 4 (November 20, 2017): 1757–74. http://dx.doi.org/10.1007/s10884-017-9627-x.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Singh, Jagadish, and Achonu Joseph Omale. "Robe’s circular restricted three-body problem with zonal harmonics." Astrophysics and Space Science 353, no. 1 (June 12, 2014): 89–96. http://dx.doi.org/10.1007/s10509-014-1995-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Bardin, B. S., and A. N. Avdyushkin. "On Stability of the Collinear Libration Point $L_{1}$ in the Planar Restricted Circular Photogravitational Three-Body Problem." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd221202.

Full text
Abstract:
The stability of the collinear libration point $L_{1}$ in the photogravitational three-body problem is investigated. This problem is concerned with the motion of a body of infinitely small mass which experiences gravitational forces and repulsive forces of radiation pressure coming from two massive bodies. It is assumed that the massive bodies move in circular orbits and that the body of small mass is located in the plane of their motion. Using methods of normal forms and KAM theory, a rigorous analysis of the Lyapunov stability of the collinear libration point lying on the segment connecting the massive bodies is performed. Conclusions on the stability are drawn both for the nonresonant case and for the case of resonances through order four.
APA, Harvard, Vancouver, ISO, and other styles
10

Kholshevnikov, Konstantin V., and Vladimir B. Titov. "Minimal velocity surface in the restricted circular Three-Body-Problem." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 65, no. 4 (2020): 734–42. http://dx.doi.org/10.21638/spbu01.2020.413.

Full text
Abstract:
In the framework of the restricted circular Three-Body-Problem, the concept of the minimum velocity surface S is introduced, which is a modification of the zero-velocity surface (Hill surface). The existence of Hill surface requires occurrence of the Jacobi integral. The minimum velocity surface, other than the Jacobi integral, requires conservation of the sector velocity of a zero-mass body in the projection on the plane of the main bodies motion. In other words, there must exist one of the three angular momentum integrals. It is shown that this integral exists for a dynamic system obtained after a single averaging of the original system by longitude of the main bodies. Properties of S are investigated. Here is the most significant. The set of possible motions of the zero-mass body bounded by the surface S is compact. As an example the surfaces S for four small moons of Pluto are considered in the framework of the averaged problem Pluto — Charon — small satellite. In all four cases, S represents a topological torus with small cross section, having a circumference in the plane of motion of the main bodies as the center line.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Circular Restricted Three Body Problem"

1

Tan, Minghu. "Low energy capture of near-Earth asteroids in the circular restricted three-body problem." Thesis, University of Glasgow, 2018. http://theses.gla.ac.uk/30779/.

Full text
Abstract:
Near-Earth Asteroids (NEAs) can provide useful resources in terms of feedstock for spacecraft propellant, crew logistic support and a range of useful metals. The possibility of capturing small NEAs using low energy transfers would therefore be of significant scientific and commercial interest. Although NEAs may make close approaches to the Earth, and so represent a potential impact threat, the exploitation of their resources has long been proposed as a necessary element for future space exploration. The objective of the research presented in this thesis is to develop methodologies for the trajectory design of capturing NEAs in the neighbourhood of the Earth. Firstly aimed at capturing NEAs around the Earth-Moon L2 point, a new type of lunar asteroid capture is defined, termed direct capture. In this capture strategy, the transfer trajectory for capturing an NEA into the Earth-Moon system is modelled in the Sun-Earth-Moon restricted four-body. A Lambert arc in the Sun-asteroid two-body problem is used as an initial guess and a differential corrector used to generate the transfer trajectory from the asteroid’s initial obit to the stable manifold associated with Earth-Moon L2 point. The direct asteroid capture strategy requires a shorter flight time compared to an indirect asteroid capture strategy, which couples capture in the Sun-Earth circular restricted three-body problem and subsequent transfer to the Earth-Moon circular restricted three-body problem. Finally, the direct and indirect asteroid capture strategies are also applied to consider capture of asteroids at the triangular libration points in the Earth-Moon system. As ideal locations for space science missions and candidate gateways for future crewed interplanetary missions, the Sun-Earth libration points L1 and L2 are also preferred locations for the captured asteroids. Therefore, the concept of coupling together a flyby of the Earth and then capturing small NEAs onto Sun–Earth L1 or L2 periodic orbits is proposed. A periapsis map is then employed to determine the required perigee of the Earth flyby. Moreover, depending on the perigee distance of the flyby, Earth flybys with and without aerobraking are investigated to design a transfer trajectory capturing a small NEA from its initial orbit to the stable manifolds associated with Sun-Earth L1 and L2 periodic orbits. NEA capture strategies using an Earth flyby with and without aerobraking both have the potential to be of lower cost in terms of energy requirements than a direct NEA capture strategy without the Earth flyby. Moreover, NEA capture with an Earth flyby also has the potential for a shorter flight time compared to the NEA capture strategy without the Earth flyby. Following by this work, a more general analysis of aerobraking is undertaken and the low energy capture of near-Earth asteroids into bound orbits around the Earth using aerobraking is then investigated. Two asteroid capture strategies utilizing aerobraking are defined, termed single-impulse capture and bi-impulse capture, corresponding to two approaches to raising the perigee height of the captured asteroid’s orbit after the aerobraking manoeuvre. A Lambert arc in the Sun-asteroid two-body problem is again used as an initial estimate for the transfer trajectory to the Earth and then a global optimization is undertaken, using the total transfer energy cost and the retrieved asteroid mass ratio (due to ablation) as objective functions. It is shown that aerobraking can in principle enable candidate asteroids to be captured around the Earth with, in some cases, extremely low energy requirements. The momentum exchange theory is also applied to the capture of small near-Earth asteroids into bound periodic orbits at the Sun-Earth L1 and L2 points. A small asteroid is first manoeuvred to engineer a flyby with a larger asteroid. Two strategies are then considered: when the small asteroid approaches the vicinity of the large asteroid, it will either impact the large asteroid or connect to it with a tether. In both strategies, momentum exchange can be used to effect the capture of one of the asteroids. Then, a two-impulse Lambert arc is utilized to design a post-encounter transfer trajectory to the stable manifolds of the Sun-Earth L1 or L2 points. By investigating the outcome of the impact on the small asteroid, or the tension of the tether, the maximum velocity increment available using these momentum exchange strategies is investigated. Again the capture strategies using momentum exchange in principle have the potential to deliver low-energy capture of asteroids. The methods presented in this thesis are intended to be used as a preliminary analysis for these asteroid capture strategies. Although some significant practical challenges remain, the transfer in the CRTBP models can serve as a good approximation for the trajectory in a more accurate dynamical model.
APA, Harvard, Vancouver, ISO, and other styles
2

Chupin, Maxime. "Interplanetary transfers with low consumption using the properties of the restricted three body problem." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066307/document.

Full text
Abstract:
Le premier objectif de cette thèse est de bien comprendre les propriétés de la dynamique du problème circulaire restreint des trois corps et de les utiliser pour calculer des missions pour satellites pourvus de moteurs à faible poussée. Une propriété fondamentale est l'existence de variétés invariantes associées à des orbites périodiques autour des points de \bsc{Lagrange}. En suivant l'idée de l'\emph{Interplanetary Transport Network}, la connaissance et le calcul des variétés invariantes, comme courants gravitationnels, sont cruciaux pour le \emph{design} de missions spatiales. Une grande partie de ce travail de thèse est consacrée au développement de méthodes numériques pour calculer le transfert entre variétés invariantes de façon optimale. Le coût que l'on cherche alors à minimiser est la norme $L^{1}$ du contrôle car elle est équivalente à minimiser la consommation des moteurs. On considère aussi la norme $L^{2}$ du contrôle car elle est, numériquement, plus facile à minimiser. Les méthodes numériques que nous utilisons sont des méthodes indirectes rendues plus robustes par des méthodes de continuation sur le coût, sur la poussée, et sur l'état final. La mise en œuvre de ces méthodes repose sur l'application du Principe du Maximum de Pontryagin. Les algorithmes développés dans ce travail permettent de calculer des missions réelles telles que des missions entre des voisinages des points de \bsc{Lagrange}. L'idée principale est d'initialiser un tir multiple avec une trajectoire admissible composée de parties contrôlées (des transferts locaux) et de parties non-contrôlées suivant la dynamique libre (les variétés invariantes). Les méthodes mises au point ici, sont efficaces et rapides puisqu'il suffit de quelques minutes pour obtenir la trajectoire optimale complète. Enfin, on développe une méthode hybride, avec à la fois des méthodes directes et indirectes, qui permettent d'ajuster la positions des points de raccord sur les variétés invariantes pour les missions à grandes variations d'énergie. Le gradient de la fonction valeur est donné par les valeurs des états adjoints aux points de raccord et donc ne nécessite pas de calculs supplémentaire. Ainsi, l'implémentation de algorithme du gradient est aisée
The first objective of this work is to understand the dynamical properties of the circular restricted three body problem in order to use them to design low consumption missions for spacecrafts with a low thrust engine. A fundamental property is the existence of invariant manifolds associated with periodic orbits around Lagrange points. Following the Interplanetary Transport Network concept, invariant manifolds are very useful to design spacecraft missions because they are gravitational currents. A large part of this work is devoted to designing a numerical method that performs an optimal transfer between invariant manifolds. The cost we want to minimize is the $L^{1}$-norm of the control which is equivalent to minimizing the consumption of the engines. We also consider the $L^{2}$-norm of the control which is easier to minimize numerically. The numerical methods are indirect ones coupled with different continuations on the thrust, on the cost, and on the final state, to provide robustness. These methods are based on the application of the Pontryagin Maximum Principal. The algorithms developed in this work allow for the design of real life missions such as missions between the realms of libration points. The basic idea is to initialize a multiple shooting method with an admissible trajectory that contains controlled parts (local transfers) and uncontrolled parts following the natural dynamics (invariant manifolds). The methods developed here are efficient and fast (less than a few minutes to obtain the whole optimal trajectory). Finally, we develop a hybrid method, with both direct and indirect methods, to adjust the position of the matching points on the invariant manifolds for missions with large energy gaps. The gradient of the value function is given by the values of the costates at the matching points and does not require any additional computation. Hence, the implementation of the gradient descent is easy
APA, Harvard, Vancouver, ISO, and other styles
3

Nicholls, Robert [Verfasser], and Urs [Akademischer Betreuer] Frauenfelder. "Second species orbits of negative action and contact forms in the circular restricted three-body problem / Robert Nicholls ; Betreuer: Urs Frauenfelder." Augsburg : Universität Augsburg, 2021. http://d-nb.info/1241474354/34.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Rosa, Ibarra Abraham de la. "Global instability in the elliptic restricted three body problem." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/277577.

Full text
Abstract:
The goal of this thesis is to show global instability or Arnold's diffusion in the elliptic restricted three body problem (ERTBP) by proving the existence of pseudo-trajectories diffusing along the phase space for certain ranges of the eccentricity of the primaries (e), the angular momentum of the comet (G) and the parameter of mass (µ). More precisely, the results presented in his thesis, are valid for G big enough, eG bounded and µ small enough. The thesis is divided in two chapters and two appendices. The chapter one, contains all the main results. After introducing the ERTBP, we use McGehee coordinates to define the infinity manifold, which turn to be a three dimensional invariant manifold in the extended phase space which behaves topologically as a Normally Hyperbolic Invariant Manifold (NHIM), although it is of parabolic type. This means that the rate of approach and departure from it along its invariant manifolds is polynomial in time, instead of exponential-like as happens in a standard NHIM. On the other hand, the inner dynamics is trivial, since it is formed by a two-parameter family of 2p-periodic orbits in the 5D extended phase space which correspond to constant solutions in the 4D phase space. As a consequence, the stable and unstable manifold of the infinity manifold are union of the stable and unstable manifolds of its periodic orbits, and as long as these manifolds intersect along transversal heteroclinic orbits, the scattering map can be defined, as De la Llave, Seara and Delshams did. Unfortunately, since the inner dynamics of the infinity manifold is so simple, the classical mechanisms of diffusion, consisting of combining the inner and outer dynamics, do not work here. Instead, as a novelty, we will be able to find two different scattering maps which will be combined in a suitable way to provide orbits whose angular momentum increases. The asymptotic formula of the scattering map relies entirely in the computation of the so called Menikov potential as defined in the works of Delshams, Gutiérrez and Seara. The first derivative of the Melnikov potential gives the first order approximation of the distance between the stable and unstable invariant manifolds of the infinity manifold whenever the parameter of mass is exponentially small. Given this setting, a series of lemmas and propositions will lead to a formula of the dominant terms of this Melnikov potential. The key idea is to compute its Fourier coefficients which will be exponentially small when the angular momentum is large and an explicit formula will be not possible, therefore and effective computation will be necessary. To do so the product eG will play a key role which lead to theorems 1.5 and 1.6, the former gives an asymptotic formula for the Melnikov potential whenever eG is samll, and the latter whenever eG is finite. Both of them requires µ to be exponentially small with respect to G, and G to be big enough. These theorems naturally produce asymptotic formulas for the scattering maps in both cases and are the base for theorems 1.15 and 1.16 which formulate the existence of pseudo-trajectories in the ERTBP. In chapter two, we provide the details and the proofs of the results concerning the asymptotic formulas, given in chapter one, for the Melnikov potential and the scattering maps, including effective bounds of every error function involved. The appendices have the more technical results needed to complete in a rigorous way every proof, but because of its nature, can be relegated to the end, to make easier to follow up the main proofs.
El objetivo de esta tesis es mostrar inestabilidad global o difusión de Arnold en el problema restringido de tres cuerpos elíptico (PTCRE) mostrando la existencia de pseudo-trayectorias difusivas en el espacio fase para ciertos rangos de la excentricidad (e), el momento angular del cometa (G) y el parámetro de masa (µ). Mas precisamente, los resultados presentados, son válidos para G suficientemente grande, eG acotado y µ suficientemente pequeño. La tesis está dividida en dos capítulos y dos apéndices. El capítulo 1, contiene todos los resultados principales. Después de introducir el PTCRE, usamos coordenadas de McGehee para definir la variedad de infinito, que será de dimensión tres en el espacio fase extendido y que topológicamente se comporta como una variedad invariante normalmente hiperbólica (NHIM), aunque es de tipo parabólico. Esto significa que la tasa de acercamiento y alejamiento de ella a lo largo de sus variedades invariantes es polinomial, en lugar de exponencial como sucede en una NHIM estándar. Por otra parte, la dinámica interior es trivial ya que está formada por una familia de orbitas con 2 parámetros y de período 2p en el espacio extendido 5D que corresponden a soluciones constantes en el espacio reducido 4D. Como consecuencia, las variedades estables e inestables de la variedad de infinito son la unión de las variedades estables e inestables de sus orbitas periódicas y siempre que estas variedades se intersequen sobre orbitas heteroclínicas transversales, el scattering map puede ser definido como hicieron De la Llave, Seara y Delshams . Desafortunadamente, ya que la dinámica interior de la variedad de infinito es muy simple, el mecanismo de difusión clásico, que consiste en combinar la dinámica interior con la exterior, no funciona aquí. En su lugar, como una novedad, seremos capaces de encontrar dos scattering maps diferentes que serán combinados de manera adecuada para producir orbitas cuyo momento angular crezca. La fórmula asintótica del scattering map recae enteramente en el cálculo del llamado potencial de Melnikov, como es definido en los trabajos de Delshams, Gutiérrez y Seara. La primer derivada del potencial de Melnikov da la aproximación a primer orden de la distancia entre las variedades estable e inestable de la variedad de infinito cuando el parámetro de masa es exponencialmente pequeño. Con este planteamiento, una serie de lemas y proposiciones conducirán a la fórmula de los términos dominantes del potencial de Melnikov. La idea clave es calcular sus coeficientes de Fourier, que serán exponencialmente pequeños cuando el momento angular es grande y una fórmula explícita no será posible, así que un cálculo efectivo será necesario. Para hacerlo, el producto eG jugará un papel clave que conducirá a los teoremas 1.5 y 1.6, el primero da una fórmula asintótica del potencial de Melnikov cuando eG es pequeño y el segundo cuando eG es finito. Ambos requieren que µ sea exponencialmente pequeño con respecto a G, y G suficientemente grande. Estos teoremas naturalmente producirán las fórmulas asintóticas de los scattering maps para ambos casos y son la base de los teoremas 1.15 y 1.16, que formulan la existencia de pseudo-trayectorias en el PTCRE. En el capítulo 2, damos los detalles y las pruebas de los resultados concernientes a las formulas asintóticas, dadas en el capítulo 1, para el potencial de Melnikov y los scattering maps, incluyendo las cotas efectivas de cada error involucrado. Los apéndices tienen los resultados mas técnicos que son necesarios para completar de forma rigurosa cada prueba, pero que por su naturaleza, pueden ser relegados al final para hacer seguir las pruebas con mas facilidad.
APA, Harvard, Vancouver, ISO, and other styles
5

Rodríguez, del Río Óscar. "Ejection-collision orbits in the restricted three-body problem." Doctoral thesis, Universitat Politècnica de Catalunya, 2021. http://hdl.handle.net/10803/672338.

Full text
Abstract:
The main objective of this dissertation is the study of the ejection-collision (EC) orbits in the circular and planar Restricted Three Body Problem (RTBP from now on). In particular, we will focus on the analytical and numerical study of a very specific type of EC orbits, that we denote as n-EC orbits. An n-EC orbit is an orbit such that the particle ejects from one primary and reaches n times a relative maximum in the distance with respect to the primary from which it ejected before colliding with it. In this way, we will study numerically in depth this kind of orbits and we will show analytically that for a sufficiently large value of the Jacobi constant (for which we will give an expression in terms of the mass parameter and the value of n) there exist exactly four n-EC orbits with well-defined characteristics. These results generalize and improve the previous results for the particular case of n=1, and we will see that they can be easily extrapolated to the Hill problem. Besides, we will observe numerically that the evolution of these four original families of n-EC orbits present a very rich dynamics.It is well-known that the system that defines the motion of the particle is not well defined at the points where the primaries are located. For this reason, we have used two different techniques to regularize the collision, the McGehee regularization and the Levi-Civita regularization. Thus, in this dissertation we have analyzed the advantages and disadvantages of each regularization and the different methods that can be used to detect collisions. Since this dissertation will be mainly focused on values of the Jacobi constant greater than those associated to the equilibrium point L1, these two local regularizations will be enough. For less restrictive values of the Jacobi constant we will see that there exist other global regularizations or alternatively, we can simply work with local regularizations in a neighbourhood of each primary.On the other hand, from the numerical point of view we have analyzed the global behaviour of the ejection orbits in the RTBP. We have studied the relation between the family of Lyapunov periodic orbits around the equilibrium point L1 and the ejection orbits for values of the Jacobi constant such that the associated Hill regions only allow a bounded motion for these orbits. In particular, we have seen that a chaotic infinity of heteroclinic connections between one primary and the Lyapunov periodic orbits around the equilibrium point L1 are obtained. As a consequence a chaotic infinity of ejection-collision orbits is also derived. Besides, we will see that we can construct colour diagrams that allow to describe the global dynamics of the ejection orbits given a range of time. These colour diagrams provide a very precise understanding of the dynamics of these orbits.Finally, we have made a first exploration of the spatial case of the circular restricted three body problem (RTBP 3D). In this first approach we have not used the classical Kustaanheimo–Stiefel regularization, instead we have decided to use a 3D version of the McGehee regularization. This presents some problems that we have analyzed and addressed,
L'objectiu principal d'aquesta dissertació és l'estudi de les òrbites d'ejecció-col·lisió (EC) al problema restringit de tres cossos circular i pla (RTBP a partir d'ara). En particular, ens centrarem en l'estudi analític i numèric d'unes òrbites d'EC molt particulars, a les quals hem anomenat òrbites de n-EC. Aquestes òrbites de n-EC, són òrbites tal que la partícula ejecta d'un primari, assoleix n màxims en la distància respecte al primari del qual han ejectat per a continuació tornar a col·lisionar amb ell. D'aquesta forma numèricament estudiarem en profunditat aquest tipus d'òrbites i analíticament demostrarem que per un valor prou gran de la constant de Jacobi (per la qual donarem una expressió en termes del paràmetre de masses i el valor de n) existeixen exactament quatre òrbites de n-EC amb unes característiques ben determinades. Aquests resultats generalitzen i milloren els resultats previs pel cas particular de n=1, i veurem que es poden extrapolar fàcilment al problema de Hill. A més, numèricament veurem que l'evolució d'aquestes quatre famílies d'òrbites de n-EC originals presenta una dinàmica molt rica.És ben sabut, que el sistema que defineix el moviment de la partícula no està ben definit als punts on es troben situats els primaris. Per aquest motiu hem utilitzat dues tècniques de regularització de la col·lisió, la regularització de McGehee i la regularització de Levi-Civita. D'aquesta forma, en aquesta memòria hem analitzat els avantatges i els inconvenients de cada regularització, i els diferents mètodes que es poden utilitzar per detectar col·lisions. Com que gran part d'aquesta memòria es focalitzarà en valors de la constant de Jacobi més grans que l'associat al punt d'equilibri L1 aquestes dues regularitzacions de caràcter local seran suficients. Per valors menys restrictius de la constant de Jacobi veurem que existeixen altres regularitzacions de caràcter global o que simplement podem treballar amb regularitzacions locals a l'entorn de cada primari.Per altra banda, numèricament hem analitzat el comportament global de les òrbites d'ejecció al RTBP. Hem estudiat la relació entre la família de les òrbites periòdiques de Lyapunov al voltant del punt d'equilibri lineal L1 i les òrbites d'ejecció que es duu a terme al rang de valors de la constant de Jacobi tals que les regions de Hill associades només permeten un moviment fitat per a aquestes òrbites. En particular, hem vist que s'obté una infinitat caòtica de connexions heteroclíniques entre un primari i l'òrbita periòdica de Lyapunov al voltant del punt d'equilibri lineal L1. Com a conseqüència, també es deriva una infinitat caòtica d'òrbites d'ejecció-col·lisió. A més, veurem que podem construir uns diagrames de color que ens permeten descriure la dinàmica global de les òrbites d'ejecció donat un interval de temps. Aquests diagrames proporcionen una comprensió molt precisa de la dinàmica d'aquestes òrbites.Finalment, hem fet una primera exploració del cas espacial del problema restringit de tres cossos circular (RTBP 3D). En aquesta primera aproximació no hem utilitzat la clàssica regularització de Kustaanheimo-Stiefel i hem decidit utilitzar una versió 3D de la regularització de McGehee. Això presenta alguns problemes, que hem analitzat i abordat, però aquesta aproximació és suficient per obtenir un primer resultat numèric sobre òrbites de 1-EC i per il·lustrar la complexitat del cas 3D.
Matemàtica aplicada
APA, Harvard, Vancouver, ISO, and other styles
6

Iuliano, Jay R. "A Solution to the Circular Restricted N Body Problem in Planetary Systems." DigitalCommons@CalPoly, 2016. https://digitalcommons.calpoly.edu/theses/1612.

Full text
Abstract:
This thesis is a brief look at a new solution to a problem that has been approached in many different ways in the past - the N body problem. By focusing on planetary systems, satellite dynamics can be modeled in a fashion similar to the Circular Restricted Three Body Problem (CR3BP) with the Circular Restricted N Body Problem (CRNBP). It was found that this new formulation of the dynamics can then utilize the tools created from all the research into the CR3BP to reassess the possibility of different complex trajectories in systems where there are more than just two large gravitational bodies affecting the dynamics, namely periodic and semi-periodic orbits, halo orbits, and low energy transfers It was also found that not only system dynamics, but models of the Jacobi constant could also be formulated similarly to the CR3BP. Validating the authenticity of these new sets of equations, the CRNBP dynamics are applied to a satellite in the Earth-Moon system and compared to a simulation of the CR3BP under identical circumstances. This test verified the dynamics of the CRNBP, showing that the two systems created almost identical results with relatively small deviations over time and with essentially identical path trends. In the Jovian system, it was found the mass ratio required to validated the assumptions required to integrate the equations of motion was around .1$\%$. Once the mass ratio grew past that limit, trajectories propagated with the CRNBP showed significant deviation from trajectories propagated with a higher fidelity model of Newtonian motion. The results from the derivation of the Jacobi constant are consistent with the 3 body system, but they are fairly standalone.
APA, Harvard, Vancouver, ISO, and other styles
7

Jedrey, Richard M. "Development of a Discretized Model for the Restricted Three-Body Problem." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306856595.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Ross, Shane David Marsden Jerrold E. "Cylindrical manifolds and tube dynamics in the restricted three-body problem /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-05182004-154045.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Soldini, Stefania. "Design and control of solar radiation pressure assisted missions in the sun-earth restricted three-body problem." Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/401834/.

Full text
Abstract:
The scientific interest in space exploration is driven by the desire to answer fundamental questions relating to the formation of our solar system and life on Earth. Space agencies are currently pushing the boundaries of space mission design to meet scientific goals. Thus, space missions require novel trajectories to further human space exploration. A modern approach that has arisen in space mission design is to use dynamical system tools that exploit the natural dynamics of the solar system. A spacecraft's natural dynamics are affected by environmental perturbations such as Solar Radiation Pressure(SRP). Traditionally, the design of space missions requires any perturbations to be counteracted through corrective manoeuvres. However, these corrective manoeuvres require propellant and therefore the pre-storing of fuel. This thesis investigates fuel-free propulsion for harnessing SRP in the design of space missions of the Sun-Earth restricted three-body problem. SRP propulsion is applied to the spacecraft's orbit control and furthermore to create the propulsion required for the design of transfers between quasi-periodic orbits and end-of-life disposal trajectories. The advantage of SRP manoeuvres is that the spacecraft can have access to an unlimited source of propellant (the Sun's radiation) consequently extending its life and reducing the overall mission costs; where the advancement in space technology makes harnessing SRP devices possible for future missions design. SRP manoeuvres are triggered by light and extended reflective deployable structures (i.e., mirror-like surfaces). The magnitude of the SRP acceleration is a function of the spacecraft's area-to-mass ratio, its reflectivity properties, mass and orientation of the reflective surface to the Sun-line direction. This thesis demonstrates that SRP manoeuvres are an effective and an effcient approach to stabilise the natural dynamics of the spacecraft in the Sun-Earth system. The size of the required reflective deployable area and spacecraft pointing accuracy are the ultimate outcomes of this research. Along with the design of the reflective area, the definition of a new control law, a method to perform transfers between quasi-periodic orbits and a strategy for the end-of-life disposal are the major important research findings.
APA, Harvard, Vancouver, ISO, and other styles
10

Kim, Seongchan [Verfasser], and Urs [Akademischer Betreuer] Frauenfelder. "J+-like invariants and families of periodic orbits in the restricted three-body problem / Seongchan Kim ; Betreuer: Urs Frauenfelder." Augsburg : Universität Augsburg, 2018. http://d-nb.info/1171705409/34.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Circular Restricted Three Body Problem"

1

Generating families in the restricted three-body problem. Berlin: Springer-Verlag, 1997.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Frauenfelder, Urs, and Otto van Koert. The Restricted Three-Body Problem and Holomorphic Curves. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72278-8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Bryuno, Aleksandr D. The restricted 3-body problem: Plane periodic orbits. New York: W.de Gruyter, 1994.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

The restricted 3-body problem: Plane periodic orbits. New York: W. de Gruyter, 1994.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Henon, Michel. Generating Families in the Restricted Three-Body Problem. Springer, 2013.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Frauenfelder, Urs, and Otto van Koert. The Restricted Three-Body Problem and Holomorphic Curves. Birkhäuser, 2018.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Generating Families in the Restricted Three-Body Problem. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44712-1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Generating Families in the Restricted Three-Body Problem. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-69650-4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Henon, Michel. Generating Families in the Restricted Three-Body Problem. Springer London, Limited, 2003.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Frauenfelder, Urs, and Otto van Koert. The Restricted Three-Body Problem and Holomorphic Curves. Birkhäuser, 2019.

Find full text
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Circular Restricted Three Body Problem"

1

Shymanchuk, Dzmitry, Alexander Shmyrov, and Vasily Shmyrov. "Construction of Connecting Trajectories in the Circular Restricted Three-Body Problem." In Lecture Notes in Control and Information Sciences - Proceedings, 501–6. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-87966-2_55.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Khan, Ayub, and Mohammad Shahzad. "Chaos Synchronization in a Circular Restricted Three Body Problem Under the Effect of Radiation." In Chaos and Complex Systems, 59–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33914-1_8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Guardia, Marcel, Pau Martín, and Tere M. Seara. "Homoclinic Solutions to Infinity and Oscillatory Motions in the Restricted Planar Circular Three Body Problem." In Progress and Challenges in Dynamical Systems, 265–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38830-9_16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Castelli, Roberto. "On the Relation Between the Bicircular Model and the Coupled Circular Restricted Three-Body Problem Approximation." In Nonlinear and Complex Dynamics, 53–68. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0231-2_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Dellnitz, Michael, Kathrin Padberg, Robert Preis, and Bianca Thiere. "Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem." In Nonlinear Science and Complexity, 99–105. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-90-481-9884-9_12.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Borunov, V. P., Yu A. Ryabov, and O. V. Surkov. "Application of Computer Algebra for Construction of Quasi-periodic Solutions for Restricted Circular Planar Three Body Problem." In Computer Algebra in Scientific Computing, 77–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11870814_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Valsecchi, G. B., E. Perozzi, A. E. Roy, and B. A. Steves. "Hunting for Periodic Orbits Close to that of the Moon in the Restricted Circular Three-Body Problem." In From Newton to Chaos, 231–34. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1085-1_21.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Celletti, Alessandra, Andrea Chessa, John Hadjidemetriou, and Giovanni Battista Valsecchi. "A Systematic Study of the Stability of Symmetric Periodic Orbits in the Planar, Circular, Restricted Three-Body Problem." In Modern Celestial Mechanics: From Theory to Applications, 239–55. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-2304-6_15.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Gurfil, Pini, and P. Kenneth Seidelmann. "The Restricted Three-Body Problem." In Celestial Mechanics and Astrodynamics: Theory and Practice, 163–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-50370-6_8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Bertotti, Bruno, and Paolo Farinella. "The Restricted Three-Body Problem." In Physics of the Earth and the Solar System, 242–55. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1916-7_12.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Circular Restricted Three Body Problem"

1

Roman, Rodica, Tiberiu Oproiu, Vasile Mioc, Cristiana Dumitrache, and Nedelia A. Popescu. "The dumb-bell’s restricted, photogravitational, circular three-body problem." In EXPLORING THE SOLAR SYSTEM AND THE UNIVERSE. AIP, 2008. http://dx.doi.org/10.1063/1.2993644.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Oshima, Kenta, and Tomohiro Yanao. "Families of Unstable Quasi-Satellite Orbits in the Spatial Circular Restricted Three-Body Problem." In 2018 Space Flight Mechanics Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-2224.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Panteleeva, Ya I. "LIDOV—KOZAI EFFECT AND CONFIGURATION STABILITY OF ALMOST CIRCULAR MOTION IN RESTRICTED THREE BODY PROBLEM." In 48-th International student's conferences "Physics of Space". Ural University Press, 2020. http://dx.doi.org/10.15826/b978-5-7996-2935-9.19.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Scott, Christopher, and David Spencer. "Stability Mapping of Distant Retrograde Orbits and Transports in the Circular Restricted Three-Body Problem." In AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-6431.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Yao Yu, Jia Jie, and Ma Kemao. "Chaining simple periodic orbits design based on invariant manifolds in the Circular Restricted Three-Body Problem." In 2010 3rd International Symposium on Systems and Control in Aeronautics and Astronautics (ISSCAA 2010). IEEE, 2010. http://dx.doi.org/10.1109/isscaa.2010.5632330.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Wu, Xiaojie, Yi Qi, Shijie Xu, Yu Wang, and Sihang Zhang. "Study of the Stability of Quasi-Satellite Orbits around Phobos in Planar Circular Restricted Three-Body Problem." In 2018 Space Flight Mechanics Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-0717.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

McCann, Brennan S., Matthew M. Wittal, and Morad Nazari. "Relative Spacecraft Position and Attitude in the Circular Restricted Three-Body Problem: TSE(3) vs. Dual Quaternions." In AIAA SCITECH 2023 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2023. http://dx.doi.org/10.2514/6.2023-0698.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Wu, Xiaojie, Yi Qi, Shijie Xu, Yu Wang, and Sihang Zhang. "Withdrawal: Study of the Stability of Quasi-Satellite Orbits around Phobos in Planar Circular Restricted Three-Body Problem." In 2018 Space Flight Mechanics Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-0717.c1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Abdulmyanov, T., M. Sokolova, and V. Usanin. "On the possibility of expanding the Tisserand constant for Jupiter-family comets in a binomial series." In ASTRONOMY AT THE EPOCH OF MULTIMESSENGER STUDIES. Proceedings of the VAK-2021 conference, Aug 23–28, 2021. Crossref, 2022. http://dx.doi.org/10.51194/vak2021.2022.1.1.019.

Full text
Abstract:
The 1st or 2nd degree binomial series expansion of the Hamiltonian of the circular restricted three-body problem expressedin terms of the Poincaré variables was used earlier to develop analytical theories of motion for the Trojan and Hilda asteroids.In the present paper we study the corresponding representation of the Tisserand constant, taking that of 6P/d’Arrest, aJupiter-family comet, as a numerical example. We show that as the 6th degree series expansion, the Tisserand constant isconserved no worse than in its conventional form.
APA, Harvard, Vancouver, ISO, and other styles
10

Szenkovits, Ferenc, Vasile Mioc, Cristiana Dumitrache, and Nedelia A. Popescu. "On the Elliptic Restricted Three-Body Problem." In EXPLORING THE SOLAR SYSTEM AND THE UNIVERSE. AIP, 2008. http://dx.doi.org/10.1063/1.2993640.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Circular Restricted Three Body Problem"

1

Gordon, Steven C. Some Results of Adding Solar Radiation Pressure Force to the Restricted Three-Body Problem. Fort Belvoir, VA: Defense Technical Information Center, September 1991. http://dx.doi.org/10.21236/ada241397.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Niebler, Rebecca. Abfallwirtschaftliche Geschäftsmodelle für Textilien in der Circular Economy. Sonderforschungsgruppe Institutionenanalyse, September 2020. http://dx.doi.org/10.46850/sofia.9783941627833.

Full text
Abstract:
This master thesis explores the challenges for waste management business models in the field of textiles regarding the requirements of the circular economy, as well as improvement potentials in the current framework conditions. It is concerned with the research question: "Is it advisable to change the frame-work conditions at meso or macro level, with regard to business models for waste management companies in the textile sector that are oriented towards the requirements of the circular economy, and - if so - in what way?” The approach of the study is based on the delta analysis of the e Society for Institutional Analysis at the Darmstadt University of Applied Sciences. It compares the target state of the normative requirements with the actual state of the textile and waste management framework conditions and attempts to identify the gaps (the delta). Based on the delta, it develops approaches that are intended to help reduce the gaps. The thesis develops three business models for the target year 2025 in different areas: an exchange platform for sorters, recyclers and designers, an automatic sorting plant and a plant for fibre-to-fibre recycling of mixed materials. It is becoming clear that these business models cannot meet the target requirements for the circular economy. The analysis identifies the remaining gaps in the framework conditions as the main problem. For example, insufficient innovation impulses and the lack of competitiveness of secondary raw materials inhibit the actors from applying and using new technologies and business models. Restricted access to knowledge and information, as well as a lack of transparency between the actors, also prove to be problematic. In order to answer the research question, the study recommends altering the framework conditions at meso and macro level. It proposes a platform for cooperation between designers, the introduction of a material declaration system and an eco-design guideline for textiles as possible development options. In addition, this work offers a matrix of criteria to help the actors test and improve their new waste management business models regarding their suitability for the circular economy. The analysis is carried out from an outsider's perspective on the entire textile industry. It therefore cannot cover and deal with all aspects and individual circumstances of each player in detail. The necessary changes in the framework conditions that have been identified can therefore be used as a basis for further investigations.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Circular Restricted Three Body Problem' for particular source types:
Journal articles Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography