Bibliographies thématiques / Lagrange circular orbit

Littérature scientifique sur le sujet « Lagrange circular orbit »

Auteur : Grafiati
Publié le 14 mars 2023

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Articles de revues sur le sujet "Lagrange circular orbit"

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Kurbasova, G., et L. Rykhlova. « The Oscillation of a System Earth – Moon ». International Astronomical Union Colloquium 178 (2000) : 493–94. http://dx.doi.org/10.1017/s0252921100061650.

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Internal links in the Earth-Moon system are determined by gravitational interaction. According to the least compulsion principle of Gauss, the deviation of “free motion” of heliocentric orbits of two material points with Earth and Moon masses is determined by the sum of the products of each material points’ deviation from its free motion and its mass.By solving the minimization problem using the Lagrange multiplier method, Lagrange equations of the first kind were obtained in vector form. With acceptable assumptions (introduction of non-dimensional time τ = nt, where n is the sidereal rotation of the Moon, and the lunar orbit is considered to be circular) the linkage coefficient (Lagrange multiplier) is:where v1and v2 are proper frequencies of the Earth and the Moon and μ is the Moon/Earth mass ratio.
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Ghazy, Mohammed, et Brett Newman. « Keeping a Spacecraft on a Vertical Circular Collinear Lagrange Point Orbit ». Journal of Guidance, Control, and Dynamics 33, no 4 (juillet 2010) : 1095–104. http://dx.doi.org/10.2514/1.47721.

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Oliveira, Thais C., et Antonio F. B. A. Prado. « SEARCH FOR STABLE ORBITS AROUND THE BINARY ASTEROID SYSTEMS 1999 KW4 AND DIDYMOS ». Revista Mexicana de Astronomía y Astrofísica 56, no 1 (1 avril 2020) : 113–28. http://dx.doi.org/10.22201/ia.01851101p.2020.56.01.12.

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This work includes analytical and numerical studies of spacecrafts orbiting two binary asteroid systems: 1999 KW4 and Didymos. The binary systems are modeled as full irregular bodies, such that the whole evolution of the results will show the impact of the irregular gravity field in the lifetime and dynamics of the spacecraft’s orbit. The equations of motion of the binary system and the spacecraft are derived from Lagrange Equations. The solar radiation pressure is consired in the dynamics of the spacecraft.Two distinct methods are used to search for stable orbits around the binary systems. One is called the grid search method, which defines the main body as a point mass to estimate the initial state of the spacecraft based on a circular Keplerian orbit. The second method is the search for periodic orbits based on zero-velocity surfaces.
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Majeed, Bushra, et Mubasher Jamil. « Dynamics and center of mass energy of colliding particles around black hole in f(R) gravity ». International Journal of Modern Physics D 26, no 05 (avril 2017) : 1741017. http://dx.doi.org/10.1142/s0218271817410176.

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We have investigated the dynamics of particles in the vicinity of a static spherically symmetric black hole in [Formula: see text] gravity. Using the Euler Lagrange method, the dynamical equations of a neutral particle are obtained. Assuming that the particle is initially moving in the innermost stable circular orbit (IMSCO), we have calculated its escape velocity, after a collision with some other particle. The conditions for the escape of colliding particles are discussed. The effective potential and the trajectories of the escaping particles are studied graphically.
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Shen, Gangqi, Yu Wang et Houjun Lü. « Space-Time Properties of Extreme RN Black Holes in Static Triangular Distribution ». Symmetry 15, no 2 (14 février 2023) : 505. http://dx.doi.org/10.3390/sym15020505.

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We studied the space-time properties of the triangular symmetric black hole in the case of extreme RN black hole. Because the neutral test particle is only affected by space-time in the curved space-time, we chose the triangular symmetric black hole as the model with which to study the motion of the test particle in this case. The curvature tensor and curvature scalar were calculated by giving the metric and the Christoffel Symbol, and then the kinematics equation of the test particle was obtained and analyzed by using these quantities. Then we analyzed the relationship between the coordinate distance and the inherent distance, the relationship between the coordinate time and the inherent time, the inherent velocity and the coordinate velocity of light, and then verified the correctness of general relativity. Next, the one-dimensional effective potential and two-dimensional effective potential of the system under different separation distances were analyzed. Finally, we analyzed and explored the innermost stable circular orbit, calculated all the Lagrange points under this model, and expounded some applications of circular orbit in astrophysics.
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Yeager, Travis, et Nathan Golovich. « MEGASIM : Lifetimes and Resonances of Earth Trojan Asteroids—The Death of Primordial ETAs ? » Astrophysical Journal 938, no 1 (1 octobre 2022) : 9. http://dx.doi.org/10.3847/1538-4357/ac8e63.

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Abstract We present an analysis of lifetimes and resonances of Earth Trojan Asteroids (ETAs) in the MEGASIM data set. Trojan asteroids co-orbit the Sun with a planet, but remain bound to the Lagrange points, L4 (60° leading the planet) or L5 (60° trailing). In the circular three-body approximation, the stability of a Trojan asteroid depends on the ratio of the host planet mass and the central mass. For the inner planets, the range of stability becomes increasingly small, so perturbations from the planets have made primordial Trojans rare. To date, there have been just two ETAs (2010 TK7 and 2020 XL5), several Mars Trojans, and a Venus Trojan discovered. The estimated lifetimes of the known inner system Trojans are shorter than a million years, suggesting they are interlopers rather than members of a stable and long-lasting population. With the largest ETA n-body simulation to date, we are able to track their survival across a wide initialized parameter space. We find that the remaining fraction of ETAs over time is well fit with a stretched exponential function that, when extrapolated beyond our simulation run time, predicts zero ETAs by 2.33 Gyr. We also show correlations between ETA ejections and the periods of the Milankovitch cycles. Though Earth’s orbital dynamics dominate the instabilities of ETAs, we provide evidence that ETA ejections are linked to resonances found in the variation of the orbital elements of many if not all of the planets.
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Xiong, J., Y. B. Jia et C. Liu. « Symmetry and Relative Equilibria of a Bicycle System ». Nelineinaya Dinamika 17, no 4 (2021) : 391–411. http://dx.doi.org/10.20537/nd210403.

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In this paper, we study the symmetry of a bicycle moving on a flat, level ground. Applying the Gibbs – Appell equations to the bicycle dynamics, we previously observed that the coefficients of these equations appeared to depend on the lean and steer angles only, and in one such equation, a term quadratic in the rear wheel’s angular velocity and a pseudoforce term would always vanish. These properties indeed arise from the symmetry of the bicycle system. From the point of view of the geometric mechanics, the bicycle’s configuration space is a trivial principal fiber bundle whose structure group plays the role of a symmetry group to keep the Lagrangian and constraint distribution invariant. We analyze the dimension relationship between the space of admissible velocities and the tangent space to the group orbit, and then employ the reduced nonholonomic Lagrange – d’Alembert equations to directly prove the previously observed properties of the bicycle dynamics. We then point out that the Gibbs – Appell equations give the local representative of the reduced dynamic system on the reduced constraint space, whose relative equilibria are related to the bicycle’s uniform upright straight or circular motion. Under the full rank condition of a Jacobian matrix, these relative equilibria are not isolated, but form several families of one-parameter solutions. Finally, we prove that these relative equilibria are Lyapunov (but not asymptotically) stable under certain conditions. However, an isolated asymptotically stable equilibrium may be achieved by restricting the system to an invariant manifold, which is the level set of the reduced constrained energy.
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Calvet, Ramon González. « On the Dynamics of the Solar System I : Orbital Inclination and Nodal Precession ». Geometry, Integrability and Quantization 23 (2022) : 1–38. http://dx.doi.org/10.7546/giq-23-2022-1-38.

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The dynamic equations of the $n$-body problem are solved in relative coordinates and applied to the solar system, whence the mean variation rates of the longitudes of the ascending nodes and of the inclinations of the planetary orbits at J2000 have been calculated with respect to the ecliptic and to the Laplace invariable plane under the approximation of circular orbits. The theory so obtained supersedes the Lagrange-Laplace secular evolution theory. Formulas for the change from the equatorial and ecliptic coordinates to those of the Laplace invariable plane are also provided.
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Welch, C. S. « Ascending node alteration of polar orbiting spacecraft using low-thrust propulsion ». Proceedings of the Institution of Mechanical Engineers, Part G : Journal of Aerospace Engineering 214, no 5 (1 mai 2000) : 313–21. http://dx.doi.org/10.1243/0954410001532088.

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This paper describes the controlled alteration of a spacecraft's orbital elements using low-thrust propulsion. It starts with a general consideration of the problem based upon Lagrange's equations and then examines its reduction to address the quasi-circular orbits appropriate to satellite emplacement. Following this, the paper describes the optimization of low-thrust manoeuvers and extends this to show that constant thrust angle techniques may be used to obtain near-optimum wedge angle and radius alterations. The alteration of ascending node is then addressed, in particular showing how the node may be altered by combined changes to inclination and altitude. This is illustrated by considering an optimum transfer between polar orbits.
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Solórzano, Carlos Renato Huaura, et Antonio Fernando Bertachini de Almeida Prado. « Third-Body Perturbation Using a Single Averaged Model : Application in Nonsingular Variables ». Mathematical Problems in Engineering 2007 (2007) : 1–14. http://dx.doi.org/10.1155/2007/40475.

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The Lagrange's planetary equations written in terms of the classical orbital elements have the disadvantage of singularities in eccentricity and inclination. These singularities are due to the mathematical model used and do not have physical reasons. In this paper, we studied the third-body perturbation using a single averaged model in nonsingular variables. The goal is to develop a semianalytical study of the perturbation caused in a spacecraft by a third body using a single averaged model to eliminate short-period terms caused by the motion of the spacecraft. This is valid if no resonance occurs with the moon or the sun. Several plots show the time histories of the Keplerian elements of equatorial and circular orbits, which are the situations with singularities. In this paper, the expansions are limited only to second order in eccentricity and for the ratio of the semimajor axis of the perturbing and perturbed bodies and to the fourth order for the inclination.
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Chapitres de livres sur le sujet "Lagrange circular orbit"

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Steane, Andrew M. « Schwarzschild–Droste solution ». Dans Relativity Made Relatively Easy Volume 2, 229–48. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.003.0017.

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The spherically symmetric vacuum solution to the Einstein field equation (Schwarzschild-Droste solution) is derived and associated physical phenomena derived and explained. It is shown how to obtain the Christoffel symbols by the Euler-Lagrange method, and hence the metric for the general spherically symmetric vacuum. Equations for general orbits are presented, and their solution for radial motion and for circular motion. Geodetic (de Sitter) precession is calculated exactly for circular orbits. The null geodesics (photon worldlines) are obtained, and the gravitational redshift. Emission from an accretion disc is calculated.
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Actes de conférences sur le sujet "Lagrange circular orbit"

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Banshchikov, A., et A. Vetrov. « Application of software tools for symbolic description and modeling of mechanical systems ». Dans The International Workshop on Information, Computation, and Control Systems for Distributed Environments. Crossref, 2020. http://dx.doi.org/10.47350/iccs-de.2020.03.

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The paper presents two software tools (graphical editor and software package). The editor is designed for the formation of a symbolic description of a mechanical system using the Lagrange formalism. A system of the absolutely rigid bodies connected by joints is considered as a mechanical system. The editor is a user interface by which one sets the structure of the interconnection of bodies (system configuration) as well as the geometric and kinematic characteristics for each body of the system. The created structure and the entered data are automatically presented in the form of a text file, which is used as an input file for the software package for modeling mechanical systems in a symbolic form with a computer. The use of these software tools is shown in detail in the example of the analysis of the dynamics of a satellite with a gravitational stabilizer in a circular orbit. For this system, the kinetic energy and force function of an approximate Newtonian gravitational field were obtained, nonlinear and linearized equations of motion were constructed, and the question of the stability of the relative equilibrium position was considered.
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Chen, Xi, et Mingfu Liao. « Steady-State Characteristics of a Dual-Rotor System With Intershaft Bearing Subjected to Mass Unbalance and Base Motions ». Dans ASME Turbo Expo 2018 : Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75215.

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A dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions is established. Using Lagrange’s principle, equations of motion for dual-rotor system relative to moving base are derived. Rotary inertia, gyroscopic inertia, transverse shear deformation, mass unbalance, and six components of deterministic base motions are taken into account. Using state-space vector, steady-state characteristics of dual-rotor system are analyzed through dual-rotor critical speed map, mode shapes, unbalance responses considering base rotations, frequency responses due to base motions, and shaft orbits. The results show that base translations just add external force vectors, while base rotations bring on parametric system matrices and additional force vectors. Base rotations not only change natural frequencies of dual-rotor system, but also break the symmetry of dynamic characteristics in the case of base lateral rotation. Excited by base harmonic translation, resonant frequencies correspond to whirl frequencies. The orbit remains circular under base axial rotation, while it becomes elliptical with a static offset under lateral rotation and then a complicated curve due to harmonic translation. When harmonic frequency of base translation gets close to dual-rotor excitation frequencies, obvious beat vibration appears. Overrall, this flexible approach can ensure calculation accuracy with high efficiency and good expandability.
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