1,721,096 research outputs found
Stability properties of the mean flow after a steady symmetry-breaking bifurcation and prediction of the nonlinear saturation
No full textIn this paper, it is shown that when a flow undergoes a steady bifurcation breaking one reflection symmetry, the mean flow obtained by averaging the two possible asymmetric flow fields resulting from the instability remains marginally stable in the postcritical regime. This property is demonstrated rigorously through an asymptotic analysis which closely follows that proposed in Sipp and Lebedev (J Fluid Mech 792:620–657, 2007) for a Hopf bifurcation with focus on wakes. In the case of wakes, the marginal stability of the mean flow is well known and had several consequences documented in the literature. To the authors’ knowledge, the marginal stability of mean flows after a symmetry-breaking pitchfork bifurcation is demonstrated here for the first time. As an example of possible consequences of marginal stability, the self-consistent model proposed for wakes in Mantič-Lugo et al. (Phys Rev Lett 113:084501, 2014) and relying on marginal stability is also applied here to the symmetry-breaking instability of the flow in a channel with a sudden expansion. For this specific case, the marginal stability of the mean flow is first demonstrated by dedicated direct numerical simulations; successively, it is shown that the resulting self-consistent model predicts the nonlinear saturation of the instability with remarkable accuracy
Solar sail trajectories to Earth’s Trojan asteroids
No full textThe recent discovery of Earth's second Trojan asteroid (2020 XL5), which will remain in the vicinity of the Sun-[Earth+Moon] triangular Lagrangian point L-4 for at least 4000 years, has attracted the attention of the scientific community as a remarkable example of those elusive objects that are the witnesses of the first phase of our Solar System. The possibility that an Earth's Trojan asteroid (ETa) may represent a pristine record of the initial conditions of the Solar System formation makes these small objects an interesting target for a robotic exploration mission. This paper analyzes orbit-to-orbit Earth-ETa transfer trajectories of an interplanetary spacecraft propelled by a solar sail. In the last decade, some pioneering space missions have confirmed the feasibility and potentiality of the solar sail concept as a propellantless propulsion system able to convert the solar radiation pressure in a continuous thrust by means of a large, lightweight and highly reflective surface. Using the state-of-the-art level of solar sail technology, this paper studies the performance of a solar-sail-based transfer trajectory toward an ETa from an optimal viewpoint and with a parametric approach
Simple solution to optimal cotangential transfer between coplanar elliptic orbits
Full text linkThe aim of this paper is to propose a semi-analytical method for the analysis of a two-impulse transfer between two coplanar elliptic orbits, assuming each maneuver to change the magnitude of the spacecraft velocity only, without affecting its direction. Using a recent mathematical model that describes the spacecraft dynamics in a compact analytical form within a two-dimensional multiple-impulse scenario, this work proposes an algorithm to calculate the global minimum velocity variation required to complete the transfer. The characteristics of the optimal transfer trajectory, which is tangent to both the parking and the target orbit, are obtained as a function of a single variable, which defines the angular position of the first maneuver. This feature allows the designer to analyze the cotangential transfer in a parametric form, thus obtaining a trade-off solution between the total velocity variation and the desired characteristics of the transfer orbit
Solar sail orbit raising with electro-optically controlled diffractive film
Full text linkThe aim of this paper is to analyze the transfer performance of a spacecraft whose primary propulsion system is a diffractive solar sail with active, switchable panels. The spacecraft uses a propellantless thruster that converts the solar radiation pressure into propulsive acceleration by taking advantage of the diffractive property of an electro-optically controlled (binary) metamaterial. The proposed analysis considers a heliocentric mission scenario where the spacecraft is required to perform a two-dimensional transfer between two concentric and coplanar circular orbits. The sail attitude is assumed to be Sun-facing, that is, with its sail nominal plane perpendicular to the incoming sunlight. This is possible since, unlike a more conventional solar sail concept that uses metalized highly reflective thin films to reflect the photons, a diffractive sail is theoretically able to generate a component of the thrust vector along the sail nominal plane also in a Sun-facing configuration. The electro-optically controlled sail film is used to change the in-plane component of the thrust vector to accomplish the transfer by minimizing the total flight time without changing the sail attitude with respect to an orbital reference frame. This work extends the mathematical model recently proposed by the authors by including the potential offered by an active control of the diffractive sail film. The paper also thoroughly analyzes the diffractive sail-based spacecraft performance in a set of classical circle-to-circle heliocentric trajectories that model transfers from Earth to Mars, Venus and Jupiter
E-Sail Option for Plunging a Spacecraft into the Sun's Atmosphere
No full textA close observation of the near-Sun region, with in situ measurements, requires that a scientific probe be placed in a heliocentric orbit with a perihelion distance on the order of a few solar radii only. This is the solution adopted by the Parker Solar Probe (PSP), whose mission design uses a very complex transfer trajectory with seven Venus gravity assists to reach a perihelion radius of roughly 9.9 solar radii in about seven years. This paper aims to discuss the capability of an Electric Solar-Wind Sail (E-sail), i.e., a propellantless propulsion system that exploits the solar wind as a deep-space thrust source using a grid of long and artificially charged tethers, to drive a scientific probe toward a heliocentric orbit with characteristics similar to that considered during the initial design of the PSP mission. The two-dimensional trajectory analysis of an E-sail-based spacecraft is performed in an optimal framework, by considering the physical constraints induced by the thermal loads acting on the propellantless propulsion system when the spacecraft approaches the inner Sun regions. This means that, during the transfer trajectory, the E-sail-based spacecraft must avoid a spherical region around the Sun whose radius depends on the mechanical characteristics of the charged tethers. The paper shows that feasible solutions, in terms of optimal transfer trajectories, are possible even when a medium-performance E-sail is considered in the spacecraft design. In that context, the obtained trajectory can drive a scientific probe on the target (high elliptic) orbit in less than two years, without the use of any intermediate flyby maneuver
Optimal Trajectories of Diffractive Sail to Highly Inclined Heliocentric Orbits
No full textRecent literature indicates that the diffractive sail concept is an interesting alternative to the more conventional reflective solar sail, which converts solar radiation pressure into a (deep space) thrust using a thin, lightweight highly reflective membrane, usually metalized. In particular, a diffractive sail, which uses a metamaterial-based membrane to diffract incoming solar rays, is able to generate a steerable thrust vector even when the sail nominal plane is perpendicular to the Sun–spacecraft line. This paper analyzes the optimal transfer performance of a diffractive-sail-based spacecraft in a challenging heliocentric scenario that is consistent with the proposed Solar Polar Imager mission concept. In this case, the spacecraft must reach a near-circular (heliocentric) orbit with a high orbital inclination with respect to the Ecliptic in order to observe and monitor the Sun’s polar regions. Such a specific heliocentric scenario, because of the high velocity change it requires, is a mission application particularly suited for a propellantless propulsion system such as the classical solar sail. However, as shown in this work, the same transfer can be accomplished using a diffractive sail as the primary propulsion system. The main contribution of this paper is the analysis of the spacecraft transfer trajectory using a near-optimal strategy by dividing the entire flight into an approach phase to a circular orbit of the same radius as the desired final orbit but with a smaller inclination, and a subsequent cranking phase until the desired (orbital) inclination is reached. The numerical simulations show that the proposed strategy is sufficiently simple to implement and can provide solutions that differ by only a few percentage points from the optimal results obtainable with a classical indirect approach
E-Sail Optimal Trajectories to Heliostationary Points
No full textThe aim of this paper is to investigate the performance of a robotic spacecraft, whose primary propulsion system is an electric solar wind sail (E-sail), in a mission to a heliostationary point (HP)—that is, a static equilibrium point in a heliocentric and inertial reference frame. A spacecraft placed at a given HP with zero inertial velocity maintains that heliocentric position provided the on-board thrust is able to counterbalance the Sun’s gravitational force. Due to the finite amount of storable propellant mass, a prolonged mission toward an HP may be considered as a typical application of a propellantless propulsion system. In this respect, previous research has been concentrated on the capability of high-performance (photonic) solar sails to reach and maintain such a static equilibrium condition. However, in the case of a solar-sail-based spacecraft, an HP mission requires a sail design with propulsive characteristics that are well beyond the capability of current or near-future technology. This paper shows that a medium-performance E-sail is able to offer a viable alternative to the use of photonic solar sails. To that end, we discuss a typical HP mission from an optimal viewpoint, by looking for the minimum time trajectory necessary for a spacecraft to reach a given HP. In particular, both two- and three-dimensional scenarios are considered, and the time-optimal mission performance is analyzed parametrically as a function of the HP heliocentric position. The paper also illustrates a potential mission application involving the observation of the Sun’s poles from such a static inertial position
Analytical solution to logarithmic spiral trajectories with circumferential thrust and mission applications
No full textThis study made use of a shape-based method to analyze the orbital dynamics of a spacecraft subject to a continuous propulsive acceleration acting along the circumferential direction. Under the assumption of a logarithmic spiral trajectory, an exact solution to the equations of motion exists, which allows the spacecraft state variables and flight time to be expressed as a function of the angular coordinate. There is also a case characterized by specific initial conditions in which the time evolution of the state variables may be analytically determined. In this context, the presented solution is used to analyze circle-to-circle trajectories, where the combination of two impulsive maneuvers and a logarithmic spiral path are used to accomplish the transfer. The determined results are then applied to the achievement of the Earth—Mars and the Earth—Venus transfers using actual data from a recent thruster developed by NASA
Optimal in-orbit repositioning of Sun-pointing Smart Dust
Full text linkA Smart Dust is a femto-spacecraft with an external surface coated with electrochromic material, which exploits the solar radiation pressure to produce a propulsive acceleration. As the optical properties of the electrochromic material change upon application of a suitable electric voltage, its propulsive acceleration may be modulated, within some limits, without the use of any propellant. This paper analyzes the optimal trajectories of a Sun-pointing Smart Dust, which provides a propulsive acceleration aligned with the Sun-spacecraft direction. In particular, the paper describes the relative motion of a Smart Dust with respect to a conventional spacecraft (the Mother Ship) that covers a heliocentric circular orbit of given radius. The Smart Dust is required to vary periodically its angular position with respect to the Mother Ship using an optimal (minimum time) strategy. This problem is addressed using an indirect approach and the optimal control law is obtained in a closed-form solution. The results discussed in this paper ensure interesting improvements over existing models from the recent literature, including the possibility of obtaining a generic phasing angle of the Smart Dust and to take into account an optimal number of on-off switchings of the electrochromic control system
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