In the present paper a fast and robust algorithm is presented for optimization of finite thrust orbit transfers.
Generally optimal nominal trajectories are designed very accurately on ground solving ...two point boundary value problems with hard numerical work and computational time.
Of course, an on board guidance system is needed to take into account the many perturbations occurring during the transfer trajectory.
Two approaches are generally followed: in the first a steering program is actuated each time the navigation system detects sensible errors from the nominal trajectory. This guidance (perturbative guidance) is not optimal.
The second approach (adaptive guidance) is to design a new optimal trajectory starting from the current state to the required final condition. This guidance is optimal but it requires the on board solution of two point boundary value problems any time it is necessary to update the trajectory.
Therefore, complex algorithms and computational times, related to the convergence of the numerical solutions, are needed.
In the present paper a method to reduce the complexity of adaptive guidance systems is described: the main point is to reduce the required two-point boundary value problems to differential problems with initial conditions only.
This allows to design a fast and easy guidance law, suitable for on-board computers with a restricted storage capability, as in the case of small satellites and small launchers.
The algorithm is robust, allowing rather large deviation from the nominal trajectory, and avoiding the use of uncontrolled iterative routines. This method is applied to an easy example: an in plane guidance law maximizing the final horizontal velocity.
In recent years, mainly due to miniaturization of electronics as well as to the improvement of computer performance, small spacecraft have increased their capabilities. More and more frequently ...specific mission objectives can be achieved with cheap satellites of reduced size. The growing use of small satellites stimulates the development of systems specifically dedicated to orbit injection of small payloads. In this context, one option is represented by air-launched rockets. The use of an air-launched rocket for delivering a small payload into the desired orbit has several advantages. First of all, payload release is much more flexible, because the delivery conditions are directly related to the dynamics of the aircraft and can be viewed as independent of ground facilities. In addition, reduced costs are associated with higher efficiency of an aircraft in the lower layers of the atmosphere with respect to traditional ground-launched rockets. To date, air-launched rockets separate from the aircraft in a horizontal flight condition. Then they maneuver in order to achieve the correct flight path angle for injecting into a gravity-turn arc of trajectory. Relevant losses are associated to this pitch maneuver; in addition, in this phase the rocket usually needs an aerodynamic control. Hence, the release of a rocket departing with a high flight path angle from the aircraft would avoid these losses and would simplify the control system, because in such a situation the pitch maneuver becomes unnecessary. This paper is aimed at investigating the dynamic behavior and performance of a payload delivered from a high performance aircraft, which flies with a high flight path angle. In particular, this work is concerned with showing the differences and tradeoffs among different starting conditions of a multistage air-launched rocket related to several flight path angles of the aircraft at release. An optimal system configuration, which allows placing a micro-satellite into a specified low Earth orbit, is proposed. This configuration is selected by optimizing the release condition, the mass distribution among the stages, and the trajectory (through the determination of the optimal control law).
Long term human space missions require artificial gravity during some phases of the space flight. In this paper we propose a dual spin system to generate artificial gravity based on a classical ...rotorcraft configuration where the rotating blade-like module provides a
1
g
-gravity at the tips. The rotating module is eventually stopped by a fluid ring damper. The dynamics and effectiveness of the damper is analyzed; in particular stability is ensured since a Lyapunov function of the system is found. Optimal damper parameters such as fluid viscosity and ring geometry are determined in order to reduce the despinning time.
Ballistic capture of spacecraft and celestial bodies by planets of the solar system is studied considering the elliptic restricted three body model. A preferential region, due to the eccentricity of ...the planet and the Sun-gravity-gradient effect is found for the capture phenomenon. An analytical formula is derived which determines the limiting value of the satellite capture eccentricity e sub(c) as a function of the pericenter distance x sub(p) and planet's true anomaly. The analytic values e sub(c) are tested by a numerical propagator, which makes use of planetary ephemeris, and only a small difference with respect to numerical integration is found. It turns out that lower values of e sub(c) occur when the planet anomaly is close to zero; that is, capture is easier when the planet is at its perihelion. This fact is confirmed by the capture of celestial bodies. It is shown that Jupiter comets are generally captured when Jupiter is in its perihelion region. Ballistic capture is also important in interplanetary missions. The propellant saved using the minimum ballistic capture eccentricity is evaluated for different missions and compared with respect to the case in which the insertion orbit is a parabola: a significant saving can be accomplished.
The motion of lunar satellites has been intensively studied in the past by interesting semi-analytical methods.
However, the poor knowledge of the Moon's gravity field makes those results incomplete. ...Subsequent lunar missions have allowed a more precise determination of the lunar gravity coefficients. Moreover, renewed scientific interest in the Moon has generated several more accurate models for the motion of a lunar orbiter.
It is known that many zonal harmonic coefficients of the Moon have the same order of
J
2 and must be included in a first-order perturbative theory. Despite of this, some success has been achieved in the study of long-term evolution of a lunar orbiter.
In particular, “frozen” orbits have been found, that is orbits whose parameters have almost vanishing long period evolution. That is, these orbits can be regarded as equilibrium configurations of the orbital dynamics, and they are of interest for the general understanding of the free motion of an orbiter as well as reference orbits, taken in order to minimize the costs of a controlled spacecraft. However, stability of these equilibria has also to be checked with respect to other perturbations of the same order, such as the effects due to the Earth and, to a lesser degree, due to the Sun.
We show that these perturbations, together with the effects induced by the lunar orbital plane motion, are rather relevant. We develop a picture analogous to the geometric approach to the motion of an Earth satellite under the influence of three poles (
J
2, Moon and Sun). The presence of more poles of perturbations (due to the other harmonics) makes the picture more complex but similar. Interesting effects on the frozen orbits as well as on the general motion of the pole and eccentricity of a lunar orbiter are found.
Recent studies demonstrate that lunar and solar gravitational assists can offer a good reduction of total variation of velocity ΔVneeded in lunar transfer trajectories. In particular the spacecraft, ...crossing regions of unstable equilibrium in the Earth--Moon--Sun system, can be guided by the Sun towards the lunar orbit with the energy needed to be captured ballistically by the Moon. The dynamics of these transfers, called weak stability boundary (WSB) transfers, will be studied here in some detail. The crucial Earth--Moon--Sun configurations allowing such transfers will be defined. The Sun's gravitational effect and lunar gravitational capture will be analyzed in terms of variations of the Jacobi 'constants' in the Earth--Sun and Earth--Moon systems. Many examples will be presented, supporting the understanding of the dynamical mechanism of WSB transfers and analytical formulas will be obtained in the case of 'quasi ballistic captures'.PUBLICATION ABSTRACT
This article presents a new method for estimating the electron temperature of the Protosphera's screw pinch. The temperature radial profile is obtained by a self-consistent modeling of a 1D MHD ...equilibrium along with a 0D power balance of the plasma column, given measurements and estimates of the axial pinch plasma current, of the plasma rotational frequency and, at the equatorial plane, of the electron density radial profile, of the edge poloidal magnetic field, of the edge electron temperature and of the neutrals pressure in the vacuum vessel. The plasma is considered in equilibrium with its neutral phase and in constant rotation. A MATLAB code has been developed with the aim of estimating the MHD radial equilibrium profiles, the thermodynamic plasma state and the neutrals profile. The numerical estimates are compared with available experimental data showing a good agreement.
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