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Articles de revues sur le sujet « Lagrange circular orbit »

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Auteur : Grafiati

Publié le 14 mars 2023

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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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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, n^o 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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Abohamer, Mohamed K., Jan Awrejcewicz, Roman Starosta, Tarek S. Amer et Mohamed A. Bek. « Influence of the Motion of a Spring Pendulum on Energy-Harvesting Devices ». Applied Sciences 11, n^o 18 (17 septembre 2021) : 8658. http://dx.doi.org/10.3390/app11188658.

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Energy harvesting is becoming more and more essential in the mechanical vibration application of many devices. Appropriate devices can convert the vibrations into electrical energy, which can be used as a power supply instead of ordinary ones. This study investigated a dynamical system that correlates with two devices, namely a piezoelectric device and an electromagnetic one, to produce two novel models. These devices are connected to a nonlinear damping spring pendulum with two degrees of freedom. The damping spring pendulum is supported by a point moving in a circular orbit. Lagrange’s equations of the second kind were utilized to obtain the equations of motion. The asymptotic solutions of these equations were acquired up to the third approximation using the approach of multiple scales. The comparison between the approximate and the numerical solutions reveals high consistency between them. The steady-state solutions were investigated, and their stabilities were checked. The influences of excitation amplitudes, damping coefficients, and the different frequencies on energy-harvesting device outputs are examined and discussed. Finally, the nonlinear stability analysis of the modulation equations is discussed through the stability and instability ranges of the frequency response curves. The work is significant due to its real-life applications, such as a power supply of sensors, charging electronic devices, and medical applications.

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Grigoriev, I. S., et A. I. Proskuryakov. « Spacecraft pulsed flights trajectories with the stages jettison into the atmosphere and phase restriction (part II) ». Engineering Journal : Science and Innovation, n^o 10 (94) (octobre 2019). http://dx.doi.org/10.18698/2308-6033-2019-9-1925.

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The paper considers the idea of reducing near-Earth space debris by discarding expended stages into the Earth’s atmosphere. The problem of optimizing the pulsed flight between the reference circular orbit of an artificial Earth satellite and the target elliptical orbit with a phase restriction on the maximum distance of the spacecraft from the Earth has been solved. Derivatives under the transversality of Lagrange principle in the process of solving are calculated by means of a specially developed technology of numerical-analytical differentiation. The first part of the paper introduces the statement and formalization of the problem. The second part of the paper studies the conditions for the optimality of Lagrange principle, analyses them and compares the findings obtained with the previously known results.

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Grigoriev, I. S., et A. I. Proskuryakov. « Optimization of spacecraft pulsed flights trajectories with the stage discharge into the atmosphere and phase restriction ». Engineering Journal : Science and Innovation, n^o 9 (93) (septembre 2019). http://dx.doi.org/10.18698/2308-6033-2019-9-1917.

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The paper considers the reducing of the near-Earth space debris due to the stages discharge into the Earth’s atmosphere, introduces the solution for optimizing the impulse transfer between the artificial Earth satellite reference circular orbit and the target elliptical orbit with a phase constraint on the maximum distance of the spacecraft from the Earth. A specially developed numerical-analytical differentiation technology allows us to calculate derivatives under the transversality of Lagrange principle. The paper proposes the transversality and stationarity conditions analysis, which results in the conclusion that the Beletsky — Egorov — Pines integral, and the Hamiltonian are continuous in the moments of all intermediate impulse actions application, including the stage discharge moments. The paper shows that the problem solution for various flight schemes coincides with a similar one without a priori assumption about the impulse effects apsidal nature.

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Papadakis, Konstantinos E., Tareq Saeed et Euaggelos E. Zotos. « Networks and Bifurcations of Eccentric Orbits in Exoplanetary Systems ». International Journal of Bifurcation and Chaos 31, n^o 13 (octobre 2021). http://dx.doi.org/10.1142/s021812742130038x.

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A systematic study of families of planar symmetric periodic orbits of the elliptic restricted three-body problem is presented, in exoplanetary systems. We find families of periodic orbits that surround only one of the primaries (Satellite-Type), that are moving around both primaries (Planet-Type), and also moving about the collinear Lagrange points. The linear stability of every periodic orbit is calculated, and the families are interpreted through stability diagrams. We focus on quasi-satellite motions of test particles that are associated with the known family [Formula: see text] that consists of 1:1 resonant retrograde Satellite-Type orbits. Over the last years, quasi-satellite orbits are of special interest due to the many applications in the design of spacecraft missions around moons and asteroids. We find the critical simple (1:1 resonant) periodic orbits of the basic families of the circular problem from which we calculate new families of the elliptic problem. Additionally, families of the elliptic problem which bifurcate from the main family [Formula: see text], for various resonances, are also presented and discussed. Hundreds of critical orbits (bifurcation points), from which families of the elliptic problem of higher multiplicity emerge, are found and the corresponding resonances are identified.

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Sapar, A. « Dynamics of Cosmic Neutrinos in Galaxies ». Open Astronomy 23, n^o 2 (1 janvier 2014). http://dx.doi.org/10.1515/astro-2017-0173.

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AbstractThe cosmic background of massive (about 1 eV rest-energy) neutrinos can be cooled to extremely low temperatures, reaching almost completely degenerated state. The Fermi velocity of the neutrinos becomes less than 100 km/s. The equations of dynamics for the cosmic background neutrinos are derived for the spherical and axisymmetrical thin circular disk galaxies. The equations comprise the gravitational potential and gravity of the uniform baryonic disk galaxies. Then the equations are integrated analytically over the disk radius. The constant radial neutrino flux in spherical galaxies favors formation of the wide unipotential wells in them. The neutrino flux in the axisymmetrical galaxies suggests to favor the evolution in the direction of a spherically symmetrical potential. The generated unipotential wells are observed as plateaux in the velocity curves of circular stellar orbits. The constant neutrino density at galactic centers gives the linear part of the curves. The derived system of quasilinear differential equations for neutrinos in the axisymmetrical galaxies have been reduced to the system of the Lagrange-Charpit equations: the coupled differential equations, specifying the local neutrino velocities and dynamics of motion along trajectories, and an additional interconnected equation of the neutrino mass conservation, which can be applied for the determination of density of the neutrino component in galaxies.

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Lu, Chung-Jen, et Chia-Hsing Hung. « Stability Analysis of a Three-Ball Automatic Balancer ». Journal of Vibration and Acoustics 130, n^o 5 (14 août 2008). http://dx.doi.org/10.1115/1.2948415.

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Ball-type automatic balancers can effectively reduce the vibrations of optical disk drives due to the inherent imbalance of the disk. Although the ball-type automatic balancer used in practice consists of several balls moving along a circular orbit, few studies have investigated the dynamic characteristics of ball-type balancers with more than two balls. The aim of this paper is to study the dynamic characteristics of a three-ball automatic balancer. Emphasis is put on the effects of the number of balls on the stability of the perfect balancing positions—the equilibrium positions where the disk is perfectly balanced. A theoretical model of an optical disk drive packed with a three-ball automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange’s equations. Closed-form formulas for the equilibrium positions are presented. The stability of the perfect balancing positions is checked with the variations for a pair of design parameters. Stable regions of the perfect balancing positions in the parameter plane of a three-ball balancer are identified and compared with those of a two-ball balancer.

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