The Experts below are selected from a list of 234 Experts worldwide ranked by ideXlab platform

Prasenjit Saha - One of the best experts on this subject based on the ideXlab platform.

  • An analytic solution for weak‐field Schwarzschild geodesics
    Monthly Notices of the Royal Astronomical Society, 2010
    Co-Authors: Daniel J. D'orazio, Prasenjit Saha
    Abstract:

    It is well known that the classical gravitational two-body problem can be transformed into a spherical harmonic oscillator by regularization. We find that a modification of the regularization transformation has a similar result to leading order in general relativity. In the resulting harmonic oscillator, the leading-order relativistic perturbation is formally a negative centrifugal force. The net centrifugal force changes sign at 3 Schwarzschild radii, which interestingly mimics the innermost stable circular orbit of the full Schwarzschild problem. Transforming the harmonic-oscillator solution back to spatial coordinates yields, for both time-like and null weak-field Schwarzschild geodesics, a solution for t, r, ϕ in terms of elementary functions of a variable that can be interpreted as a generalized Eccentric Anomaly. The textbook expressions for relativistic precession and light deflection are easily recovered. We suggest how this solution could be combined with additional perturbations into numerical methods suitable for applications such as relativistic accretion or dynamics of the Galactic Centre stars.

Daniel J. D'orazio - One of the best experts on this subject based on the ideXlab platform.

  • An analytic solution for weak‐field Schwarzschild geodesics
    Monthly Notices of the Royal Astronomical Society, 2010
    Co-Authors: Daniel J. D'orazio, Prasenjit Saha
    Abstract:

    It is well known that the classical gravitational two-body problem can be transformed into a spherical harmonic oscillator by regularization. We find that a modification of the regularization transformation has a similar result to leading order in general relativity. In the resulting harmonic oscillator, the leading-order relativistic perturbation is formally a negative centrifugal force. The net centrifugal force changes sign at 3 Schwarzschild radii, which interestingly mimics the innermost stable circular orbit of the full Schwarzschild problem. Transforming the harmonic-oscillator solution back to spatial coordinates yields, for both time-like and null weak-field Schwarzschild geodesics, a solution for t, r, ϕ in terms of elementary functions of a variable that can be interpreted as a generalized Eccentric Anomaly. The textbook expressions for relativistic precession and light deflection are easily recovered. We suggest how this solution could be combined with additional perturbations into numerical methods suitable for applications such as relativistic accretion or dynamics of the Galactic Centre stars.

Daniel J. Scheeres - One of the best experts on this subject based on the ideXlab platform.

  • Fourier Coefficient Selection for Low-Thrust Control Shaping
    Journal of Guidance Control and Dynamics, 2013
    Co-Authors: Jennifer Hudson, Daniel J. Scheeres
    Abstract:

    a = semimajor axis E = Eccentric Anomaly e = Eccentricity F = thrust acceleration FR;W;S = radial, normal, and circumferential thrust acceleration i = inclination M = mean Anomaly r = radial unit vector ŵ = normal unit vector α k = cosine coefficient, Fourier series of thrust acceleration β k = sine coefficient, Fourier series of thrust acceleration ΔV = velocity increment λ = angle of thrust acceleration Ω = longitude of the ascending node ω = argument of periapsis

  • Orbital Targeting Using Reduced Eccentric Anomaly Low-Thrust Coefficients
    Journal of Guidance Control and Dynamics, 2011
    Co-Authors: Jennifer Hudson, Daniel J. Scheeres
    Abstract:

    A method to evaluate the trajectory dynamics of low-thrust spacecraft is applied to targeting and optimal control problems. Averaged variational equations for the osculating orbital elements are used to estimate a spacecraft trajectory over many spiral orbits. Fourteen Fourier coefficients of the thrust acceleration vector represent the fundamental trajectory dynamics. Spacecraft targeting problems are solved using the averaged variational equations and a general cost function represented as a Fourier series. The resulting fuel costs and dynamic fidelity of the targeting solutions are evaluated. The goal of the method is not precise targeting, but easy reconstruction of the basic elements of the thrusting trajectory and control law.

  • Reduction of Low-Thrust Continuous Controls for Trajectory Dynamics
    Journal of Guidance Control and Dynamics, 2009
    Co-Authors: Jennifer Hudson, Daniel J. Scheeres
    Abstract:

    A novel method to evaluate the trajectory dynamics of low-thrust spacecraft is developed. The thrust vector components are represented as Fourier series in Eccentric Anomaly, and Gauss's variational equations are averaged over one orbit to define a set of secular equations. These secular equations are a function of only 14 of the thrust Fourier coefficients, regardless of the order of the original Fourier series, and are sufficient to accurately determine a low-thrust spiral trajectory with significantly reduced computational requirements as compared with integration of the full Newtonian problem. This method has applications to low-thrust spacecraft targeting and optimal control problems.

  • Trajectory Optimization Using the Reduced Eccentric Anomaly Low-Thrust Coefficients
    AIAA AAS Astrodynamics Specialist Conference and Exhibit, 2008
    Co-Authors: Jennifer Hudson, Daniel J. Scheeres
    Abstract:

    A method to evaluate the trajectory dynamics of low-thrust spacecraft is refined and applied to targeting and optimal control problems. The original method uses averaged variational equations for the osculating orbital elements with 14 Fourier coefficients of the thrust acceleration vector to estimate a spacecraft trajectory over many spiral orbits. The accuracy of this method is improved by correction of any offset of the averaged trajectory from the true trajectory due to non-trivial periodic components. Spacecraft targeting problems are then solved using the corrected averaged variational equations and a general cost function represented as a Fourier series. A method for reducing the cost of a transfer by selection of acceleration Fourier coefficients beyond the 14 that appear in the averaged equations is described.

László Á. Gergely - One of the best experts on this subject based on the ideXlab platform.

  • An Efficient Method for the Evaluation of Secular Effects in the Perturbed Keplerian Motion
    The Astrophysical Journal Supplement Series, 2006
    Co-Authors: László Á. Gergely, Zoltán Keresztes, Balázs Mikóczi
    Abstract:

    Binary systems subject to generic perturbations evolve on quasiperiodic orbits. We derive the most generic class of perturbations, which allow to evaluate secular effects via generalized complex true and Eccentric Anomaly parameters, by use of the residue theorem. Such perturbations include both the generic Brumberg force and various linear contributions to the conservative dynamics of compact binaries, up to the second post-Newtonian order. As an example, we compute the self-spin contribution to the luminosity due to gravitational radiation of a compact binary consisting of galactic black holes, the most important type of source for LISA. This translates to simply calculate the residue of the instantaneous energy loss in the origin of the complex parameter plane, which illustrates the power of the presented method.

  • Gravitational radiation reaction in compact binary systems: Contribution of the quadrupole-monopole interaction
    Physical Review D, 2003
    Co-Authors: László Á. Gergely, Zoltán Keresztes
    Abstract:

    The radiation reaction in compact spinning binaries on Eccentric orbits due to the quadrupole-monopole interaction is studied. This contribution is of second post-Newtonian order. As a result of the precession of spins the magnitude L of the orbital angular momentum is not conserved. Therefore a proper characterization of the perturbed radial motion is provided by the energy E and angular average L. As powerful computing tools, the generalized true and Eccentric Anomaly parametrizations are introduced. Then the secular losses in energy and magnitude of the orbital angular momentum together with the secular evolution of the relative orientations of the orbital angular momentum and spins are found for Eccentric orbits by use of the residue theorem. The circular orbit limit of the energy loss agrees with Poisson's earlier result. ©2003 The American Physical Society.

  • GENERALIZED TRUE- AND Eccentric-Anomaly PARAMETRIZATIONS FOR THE PERTURBED KEPLER MOTION
    The Ninth Marcel Grossmann Meeting, 2002
    Co-Authors: László Á. Gergely, Zoltán Perjés, Mátyás Vasúth
    Abstract:

    The true- and Eccentric-Anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A toolbox of methods for averaging observables in terms of the energy E and angular momentum L is developed. A broad range of systems governed by the generic Brumberg force, as well as recent applications of the theory of gravitational radiation involve integrals over a period of motion. These integrals are evaluated by using the residue theorem. It is shown that the pole of the integrand is located in the origin and that under certain circumstances an additional pole emerges.

  • The true and Eccentric Anomaly parametrizations of the perturbed Kepler motion
    The Astrophysical Journal Supplement Series, 2000
    Co-Authors: László Á. Gergely, Zoltán Perjés, Mátyás Vasúth
    Abstract:

    The true and Eccentric Anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits, by considering perturbations of the radial part of the kinetic energy in a form of a series of negative powers of the orbital radius. A toolchest of methods for averaging observables as functions of the energy $E$ and angular momentum $L$ is developed. A broad range of systems governed by the generic Brumberg force and recent applications in the theory of gravitational radiation involve integrals of these functions over a period of motion. These integrals are evaluated by using the residue theorem. In the course of this work two important questions emerge: (1) When does the true and Eccentric Anomaly parameter exist? (2) Under what circumstances and why are the poles in the origin? The purpose of this paper is to find the answer to these queries.

Mátyás Vasúth - One of the best experts on this subject based on the ideXlab platform.

  • GENERALIZED TRUE- AND Eccentric-Anomaly PARAMETRIZATIONS FOR THE PERTURBED KEPLER MOTION
    The Ninth Marcel Grossmann Meeting, 2002
    Co-Authors: László Á. Gergely, Zoltán Perjés, Mátyás Vasúth
    Abstract:

    The true- and Eccentric-Anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A toolbox of methods for averaging observables in terms of the energy E and angular momentum L is developed. A broad range of systems governed by the generic Brumberg force, as well as recent applications of the theory of gravitational radiation involve integrals over a period of motion. These integrals are evaluated by using the residue theorem. It is shown that the pole of the integrand is located in the origin and that under certain circumstances an additional pole emerges.

  • The true and Eccentric Anomaly parametrizations of the perturbed Kepler motion
    The Astrophysical Journal Supplement Series, 2000
    Co-Authors: László Á. Gergely, Zoltán Perjés, Mátyás Vasúth
    Abstract:

    The true and Eccentric Anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits, by considering perturbations of the radial part of the kinetic energy in a form of a series of negative powers of the orbital radius. A toolchest of methods for averaging observables as functions of the energy $E$ and angular momentum $L$ is developed. A broad range of systems governed by the generic Brumberg force and recent applications in the theory of gravitational radiation involve integrals of these functions over a period of motion. These integrals are evaluated by using the residue theorem. In the course of this work two important questions emerge: (1) When does the true and Eccentric Anomaly parameter exist? (2) Under what circumstances and why are the poles in the origin? The purpose of this paper is to find the answer to these queries.

  • the true and Eccentric Anomaly parameterizations of the perturbed kepler motion
    Astrophysical Journal Supplement Series, 2000
    Co-Authors: L Gergely, Zoltán Perjés, Mátyás Vasúth
    Abstract:

    The true- and Eccentric-Anomaly parameterizations of the Kepler motion are generalized to quasi-periodic orbits, by considering perturbations of the radial part of the kinetic energy in the form of a series of negative powers of the orbital radius. A toolbox of methods for averaging observables as functions of the energy E and angular momentum L is developed. A broad range of systems governed by the generic Brumberg force, as well as recent applications in the theory of gravitational radiation, involve integrals of these functions over a period of motion. These integrals are evaluated by using the residue theorem. In the course of this work, two important questions emerge: (1) When do the true- and Eccentric-Anomaly parameters exist? (2) Under what circumstances, and why, are the poles in the origin? The purpose of this paper is to find the answer to these queries.