The Experts below are selected from a list of 240 Experts worldwide ranked by ideXlab platform
Toshio Fukushima - One of the best experts on this subject based on the ideXlab platform.
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New Two-Body Regularization
The Astronomical Journal, 2006Co-Authors: Toshio FukushimaAbstract:We present a new scheme to regularize a three-dimensional two-body problem under perturbations. It is a combination of Sundman's time transformation and Levi-Civita's spatial coordinate transformation applied to the two-dimensional components of the position and velocity Vectors in the osculating orbital plane. We adopt a coordinate triad specifying the plane as a function of the orbital Angular Momentum Vector only. Since the magnitude of the orbital Angular Momentum is explicitly computed from the in-the-plane components of the position and velocity Vectors, only two components of the orbital Angular Momentum Vector are to be determined. In addition to these, we select the total energy of the two-body system and the physical time as additional components of the new variables. The equations of motion of the new variables have no singularity even when the mutual distance is extremely small, and therefore, the new variables are suitable to deal with close encounters. As a result, the number of dependent variables in the new scheme becomes eight, which is significantly smaller than the existing schemes to avoid close encounters: two less than the Kustaanheimo-Stiefel and the Burdet-Ferrandiz regularizations, and five less than the Sperling-Burdet/Burdet-Heggie regularization.
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efficient orbit integration by linear transformation for consistency of kepler energy full laplace integral and Angular Momentum Vector
The Astronomical Journal, 2004Co-Authors: Toshio FukushimaAbstract:By adopting a general linear transformation as the method of manifold correction, we modify our dual scaling method to integrate quasi-Keplerian orbits numerically. The new method adjusts the integrated position and velocity at each integration step in order to exactly satisfy the relations for the Kepler energy, Angular Momentum Vector, and the full Laplace Vector. In the case of no perturbation, the integration errors in all the orbital elements except the mean longitude at the epoch, which grows linearly with time, are reduced to the level of the machine epsilon throughout the integration. For perturbed orbits, the integration errors in position are smaller than with the previous methods of manifold correction. Since its wide applicability is unchanged and the cost of additional computation is similarly negligible, we recommend the new method as the best of our methods of manifold correction.
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FURTHER SIMPLIFICATION OF THE MANIFOLD CORRECTION METHOD FOR ORBIT INTEGRATION
The Astronomical Journal, 2004Co-Authors: Toshio FukushimaAbstract:By introducing some quantities defined on the moving orbital plane, we have developed three ways to further reduce the number of variables in our two simplified methods of manifold correction, from nine to seven or six per celestial body. Among these, the simplest option uses a set of six variables consisting of the three-dimensional orbital Angular Momentum Vector, the two independent components of the Laplace integral Vector on the moving orbital plane, and a true orbital longitude measured from an origin solely determined from the orbital Angular Momentum Vector. This scheme no longer requires any manifold correction, as does the standard method to integrate the Cartesian coordinates and velocity. However, the new method is much more precise than the standard method. For example, the longitude error of Mercury in a simultaneous integration of the Sun and nine major planets with a step size of 1.4 days exceeds 360° after a few thousand years when using the standard method but remains at the milliarcsecond level if the new method is used. In addition, the new method achieves better performance than any of the manifold correction methods we have developed, as long as round-off errors are negligible.
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EFFICIENT ORBIT INTEGRATION BY SCALING AND ROTATION FOR CONSISTENCY OF KEPLER ENERGY LAPLACE INTEGRAL AND Angular Momentum DIRECTION
The Astronomical Journal, 2003Co-Authors: Toshio FukushimaAbstract:By adding the orbital Angular Momentum Vector as another auxiliary quantity to be integrated, we extend our scaling methods to integrate quasi-Keplerian orbits numerically in order to suppress the growth of integration errors in the inclination and the longitude of the ascending node. This time, the method follows the time evolution of the Angular Momentum Vector, as well as the time development of the Kepler energy and/or the Laplace integral, in addition to integrating the usual equation of motion. By using a rotation that is independent of the application of the spatial scaling, the new method adjusts the position and velocity integrated rigorously at each integration step in order to align both perpendicular to the integrated Angular Momentum Vector. The direction and the angle of the rotation are determined uniquely from the position, the velocity, and the Angular Momentum Vector integrated. As with the original scaling methods, the new method is simple to implement, fast to compute, and applicable to a wide variety of integration methods, perturbation types, and complexities of problems. Although this addition provides no significant decrease in the position error, the new method is superior to the original scaling methods in the sense that it enhances the quality of the integration by significantly reducing the errors of the orbital plane at the cost of a negligibly small amount of additional computation.
Xavier Chapuisat - One of the best experts on this subject based on the ideXlab platform.
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Principal-axis hyperspherical description of N-particle systems : quantum-mechanical treatment
Physical Review A, 1992Co-Authors: Xavier ChapuisatAbstract:Principal-axis hyperspherical coordinates (made up of one hyperradius and 3N-7 angles as internal coordinates) and three Euler angles as external (rotational) coordinates [X. Chapuisat and A. Nauts, Phys. Rev. 44, 1328 (1991)], are used to describe an N-particle system. The exact quantum-mechanical Hamiltonian of the system in terms of these coordinates is established and is very simple. Generalized Angular-Momentum Vector operators, which allow the generation of a profitable standard representation for the Angular part of the problem, are introduced. The corresponding matrix representation of the Hamiltonian operator is built
M A C Perryman - One of the best experts on this subject based on the ideXlab platform.
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the gaia inertial reference frame and the tilting of the milky way disk
The Astrophysical Journal, 2014Co-Authors: M A C Perryman, David N Spergel, L LindegrenAbstract:While the precise relationship between the Milky Way disk and the symmetry planes of the dark matter halo remains somewhat uncertain, a time-varying disk orientation with respect to an inertial reference frame seems probable. Hierarchical structure formation models predict that the dark matter halo is triaxial and tumbles with a characteristic rate of similar to 2 rad H-0(-1) (similar to 30 mu as yr(-1)). These models also predict a time-dependent accretion of gas, such that the Angular Momentum Vector of the disk should be misaligned with that of the halo. These effects, as well as tidal effects of the LMC, will result in the rotation of the Angular Momentum Vector of the disk population with respect to the quasar reference frame. We assess the accuracy with which the positions and proper motions from Gaia can be referred to a kinematically non-rotating system, and show that the spin Vector of the transformation from any rigid self-consistent catalog frame to the quasi-inertial system defined by quasars should be defined to better than 1 mu as yr(-1). Determination of this inertial frame by Gaia will reveal any signature of the disk orientation varying with time, improve models of the potential and dynamics of the Milky Way, test theories of gravity, and provide new insights into the orbital evolution of the Sagittarius dwarf galaxy and the Magellanic Clouds. (Less)
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the gaia inertial reference frame and the tilting of the milky way disk
arXiv: Astrophysics of Galaxies, 2014Co-Authors: M A C Perryman, David N Spergel, L LindegrenAbstract:While the precise relationship between the Milky Way disk and the symmetry planes of the dark matter halo remains somewhat uncertain, a time-varying disk orientation with respect to an inertial reference frame seems probable. Hierarchical structure formation models predict that the dark matter halo is triaxial and tumbles with a characteristic rate of ~2 rad/Hubble time (~30 muas/yr). These models also predict a time-dependent accretion of gas, such that the Angular Momentum Vector of the disk should be misaligned with that of the halo. These effects, as well as tidal effects of the LMC, will result in the rotation of the Angular Momentum Vector of the disk population with respect to the quasar reference frame. We assess the accuracy with which the positions and proper motions from Gaia can be referred to a kinematically non-rotating system, and show that the spin Vector of the transformation from any rigid self-consistent catalog frame to the quasi-inertial system defined by quasars should be defined to better than 1 muas/yr. Determination of this inertial frame by Gaia will reveal any signature of the disk orientation varying with time, improve models of the potential and dynamics of the Milky Way, test theories of gravity, and provide new insights into the orbital evolution of the Sagittarius dwarf galaxy and the Magellanic Clouds.
Pavel Krasil Nikov - One of the best experts on this subject based on the ideXlab platform.
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fast non resonance rotations of spacecraft in restricted three body problem with magnetic torques
International Journal of Non-linear Mechanics, 2015Co-Authors: Pavel Krasil NikovAbstract:Abstract Fast non-resonance rotations of spacecraft around center of mass in restricted three body problem with magnetic torques are considered. It is supposed that one of primary bodies has a magnetic field, the spacecraft has magnets such that the magnetic torque is constant in the frame connected with spacecraft. In addition, it is supposed that spacecraft orbit is described by quasi-periodic functions of time, the Angular speed of spacecraft rotations much more than the elliptical mean motion of primary bodies. The averaged Hamiltonian of problem is obtained. For different parameters Dj which are functionals on a set of spacecraft orbits, the evolution of Angular Momentum Vector of spacecraft is investigated. It is shown that the increase of the magnetic torque leads to the magnification of the inclination for Angular Momentum Vector. In limiting case when gravitational torques can be neglected, the Angular Momentum Vector will be parallel to the plane of the rotation of primary bodies. It is shown that there is a mathematical analogy between the purely magnetic rotations and gravitational rotations in plane orbits whenever bifurcation parameter N is unit.
L Lindegren - One of the best experts on this subject based on the ideXlab platform.
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the gaia inertial reference frame and the tilting of the milky way disk
The Astrophysical Journal, 2014Co-Authors: M A C Perryman, David N Spergel, L LindegrenAbstract:While the precise relationship between the Milky Way disk and the symmetry planes of the dark matter halo remains somewhat uncertain, a time-varying disk orientation with respect to an inertial reference frame seems probable. Hierarchical structure formation models predict that the dark matter halo is triaxial and tumbles with a characteristic rate of similar to 2 rad H-0(-1) (similar to 30 mu as yr(-1)). These models also predict a time-dependent accretion of gas, such that the Angular Momentum Vector of the disk should be misaligned with that of the halo. These effects, as well as tidal effects of the LMC, will result in the rotation of the Angular Momentum Vector of the disk population with respect to the quasar reference frame. We assess the accuracy with which the positions and proper motions from Gaia can be referred to a kinematically non-rotating system, and show that the spin Vector of the transformation from any rigid self-consistent catalog frame to the quasi-inertial system defined by quasars should be defined to better than 1 mu as yr(-1). Determination of this inertial frame by Gaia will reveal any signature of the disk orientation varying with time, improve models of the potential and dynamics of the Milky Way, test theories of gravity, and provide new insights into the orbital evolution of the Sagittarius dwarf galaxy and the Magellanic Clouds. (Less)
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the gaia inertial reference frame and the tilting of the milky way disk
arXiv: Astrophysics of Galaxies, 2014Co-Authors: M A C Perryman, David N Spergel, L LindegrenAbstract:While the precise relationship between the Milky Way disk and the symmetry planes of the dark matter halo remains somewhat uncertain, a time-varying disk orientation with respect to an inertial reference frame seems probable. Hierarchical structure formation models predict that the dark matter halo is triaxial and tumbles with a characteristic rate of ~2 rad/Hubble time (~30 muas/yr). These models also predict a time-dependent accretion of gas, such that the Angular Momentum Vector of the disk should be misaligned with that of the halo. These effects, as well as tidal effects of the LMC, will result in the rotation of the Angular Momentum Vector of the disk population with respect to the quasar reference frame. We assess the accuracy with which the positions and proper motions from Gaia can be referred to a kinematically non-rotating system, and show that the spin Vector of the transformation from any rigid self-consistent catalog frame to the quasi-inertial system defined by quasars should be defined to better than 1 muas/yr. Determination of this inertial frame by Gaia will reveal any signature of the disk orientation varying with time, improve models of the potential and dynamics of the Milky Way, test theories of gravity, and provide new insights into the orbital evolution of the Sagittarius dwarf galaxy and the Magellanic Clouds.