Optimization of spacecraft pulsed flights trajectories with the stage discharge into the atmosphere and phase restriction

Abstract

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.

Inserting a Maximum-Mass Spacecraft into a Target Orbit Using a Limited-Thrust Engine with Releasing the Separable Part of Its Launch Vehicle into the Earth’s Atmosphere

“…The trajectory structure is determined based on the previous studies [1,[8][9][10]. The main advantage of the given-structure trajectory approach is that it yields Pontryagin extremals: under a "good" computational scheme for the shooting method and a "good" initial approximation, the modified Newton's method converges in a few iterations.…”

“…After performing the second series of maneuvers, the spacecraft is in a target orbit from which the characteristic velocity of final ascent maneuvers to the GEO is bounded by a given value. According to the earlier studies [1,[8][9][10], the cost of releasing is small for the bi-elliptical final ascent scheme. In the target orbit, the satellite is separated from the CB.…”

“…If the characteristic velocity of the final ascent maneuver is less than 1.47 km/s, the trajectory structure changes and the cost of releasing the AFT and CB into the atmosphere becomes significant. In the next step [9,10], the problem was solved without assuming the apsidality of impulse actions. It was established that in the problem with a phase constraint on the maximum possible distance between the spacecraft and the Earth and an unlimited transfer time, the solution is apsidal and coincides with that obtained in the previous step.…”

Spacecraft pulsed flights trajectories with the stages jettison into the atmosphere and phase restriction (part II)

“…Введение. Импульсная постановка задачи перелета космического аппарата (КА) с опорной орбиты на целевую эллиптическую с фазовым ограничением на максимальное удаление КА от Земли, формализация задачи и общее описание результатов приведены в первой части статьи [1]. Вторая часть статьи посвящена анализу необходимых условий оптимальности принципа Лагранжа и сравнению с уже известными результатами.…”

“…Применение принципа Лагранжа к решаемой задаче рассмотрим для случая импульса довыведения 1,5 км/c (определяет последовательность моментов 1 1 2 2 0 τ τ < < < < < < R t t t T ) [1]:…”