A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rota...A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital elements.The resulted solution is expressed in terms of two different sets of orbital elements.The first one is the classical orbital elements and the second one is the nonsingular orbital elements.Among of them,however,the semi-latus rectum and true anomaly are used due to their generality,rather than the semi-major axis and mean anomaly that are used in most references.This specific selection for orbital elements yields a new solution that is universally applicable to elliptic,parabolic and hyperbolic orbits.It is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner–Hempel equations.A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner–Hempel equations is constructed.Finally,the presented solution is validated through comparison with a high-fidelity numerical orbit propagator.The numerical results demonstrate that the new solution is computationally effective;and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.展开更多
The high performance solar sail can enable fast missions to the outer solar system and produce exotic non-Keplerian orbits.As there is no fuel consumption,mission trajectories for solar sail spacecraft are typically o...The high performance solar sail can enable fast missions to the outer solar system and produce exotic non-Keplerian orbits.As there is no fuel consumption,mission trajectories for solar sail spacecraft are typically optimized with respect to flight time.Several investigations focused on interstellar probe missions have been made,including optimal methods and new objective functions. Two modes of interstellar mission trajectories,namely 'direct flyby' and 'angular momentum reversal trajectory',are compared and discussed.As a foundation,a 3D non-dimensional dynamic model for an ideal plane solar sail is introduced as well as an optimal control framework.A newly found periodic double angular momentum reversal trajectory is presented,and some properties and potential applications of this kind of inverse orbits are illustrated.The method how to achieve the minimum periodic inverse orbit is also briefly elucidated.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.61403416)the“The Hundred Talents Program”of Chinese Academy of Science.
文摘A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital elements.The resulted solution is expressed in terms of two different sets of orbital elements.The first one is the classical orbital elements and the second one is the nonsingular orbital elements.Among of them,however,the semi-latus rectum and true anomaly are used due to their generality,rather than the semi-major axis and mean anomaly that are used in most references.This specific selection for orbital elements yields a new solution that is universally applicable to elliptic,parabolic and hyperbolic orbits.It is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner–Hempel equations.A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner–Hempel equations is constructed.Finally,the presented solution is validated through comparison with a high-fidelity numerical orbit propagator.The numerical results demonstrate that the new solution is computationally effective;and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.
基金supported by the National Natural Science Foundation of China(10832004 and 10902056)
文摘The high performance solar sail can enable fast missions to the outer solar system and produce exotic non-Keplerian orbits.As there is no fuel consumption,mission trajectories for solar sail spacecraft are typically optimized with respect to flight time.Several investigations focused on interstellar probe missions have been made,including optimal methods and new objective functions. Two modes of interstellar mission trajectories,namely 'direct flyby' and 'angular momentum reversal trajectory',are compared and discussed.As a foundation,a 3D non-dimensional dynamic model for an ideal plane solar sail is introduced as well as an optimal control framework.A newly found periodic double angular momentum reversal trajectory is presented,and some properties and potential applications of this kind of inverse orbits are illustrated.The method how to achieve the minimum periodic inverse orbit is also briefly elucidated.
