A revisited and general Kane’s formulation applied to very flexible multibody spacecraft

Abstract. Current space missions require predicting the spacecraft dynamics with considerable reliability. Among the various components of a spacecraft, subsystems like payload, structures, and power depend heavily on the dynamic behavior of the satellite during its operational life. Therefore, to ensure that the results obtained through numerical simulations correspond to the actual behavior, an accurate dynamical model must be developed. In this context, an implementation of Kane’s method is presented to derive the dynamical equations of a spacecraft composed of both rigid and flexible bodies connected via joints in tree topology. Starting from the kinematics of two generic interconnected bodies, a systematic approach is derived and the recursive structure of the equations is investigated. The Kane’s formulation allows a relatively simple derivation of the equation of motion while obtaining the minimum set of differential equations, which implies lower computational time. On the other hand, this formulation excludes reaction forces and torques from the dynamical equations. Nevertheless, in this work a strategy to compute them a posteriori without further numerical integrations is presented. Flexibility is introduced through the standard modal decomposition technique, so that modal shapes obtained by FEA software can be directly utilized to characterize the elastic motion of the flexible bodies. A spacecraft composed of a rigid bus and several flexible appendages is modeled and numerical simulations point out that this systematic method is very effective for this illustrative example

Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit

This paper considers a spacecraft pursuit-evasion problem taking place in low earth orbit. The problem is formulated as a zero-sum differential game in which there are two players, a pursuing spacecraft that attempts to minimize a payoff, and an evading spacecraft that attempts to maximize the same payoff. We introduce two associated optimal control problems and show that a saddle point for the differential game exists if and only if the two optimal control problems have the same optimal value. Then, on the basis of this result, we propose two computational methods for determining a saddle point solution: a semi-direct control parameterization method (SDCP method), which is based on a piecewise-constant control approximation scheme, and a hybrid method, which combines the new SDCP method with the multiple shooting method. Simulation results show that the proposed SDCP and hybrid methodsare superior to the semi-direct collocation nonlinear programming method (SDCNLP method), which is widely used to solve pursuit-evasion problems in the aerospace field

Eteokles in Spain? On Brecht’s Mein Bruder war ein Flieger

One of Bertolt Brecht’s most famous poems, Mein Bruder war ein Flieger, is often invoked as a manifesto for pacifist ideals, but some essential questions (who is the lyric I? what is the literal meaning of the poem?) have hardly received any attention. By evoking the poem’s nature as a Kinderlied, the context of its first publication, and its relationship with Brecht’s play Die Gewehre der Frau Carrar, this article tentatively identifies the source of its final pointe in a famous passage of Aeschylus’ Seven against Thebes, thereby suggesting—on the basis of textual comparisons—an example of far-reaching, ideological Antikerezeption in Brecht’s oeuvre, working all the way down to his Kalendergeschichten and to his Antigone

Actin Assembly at Model-Supported Lipid Bilayers

We report on the use of supported lipid bilayers to reveal dynamics of actin polymerization from a nonpolymerizing subphase via cationic phospholipids. Using varying fractions of charged lipid, lipid mobility, and buffer conditions, we show that dynamics at the nanoscale can be used to control the self-assembly of these structures. In the case of fluid-phase lipid bilayers, the actin adsorbs to form a uniform two-dimensional layer with complete surface coverage whereas gel-phase bilayers induce a network of randomly oriented actin filaments, of lower coverage. Reducing the pH increased the polymerization rate, the number of nucleation events, and the total coverage of actin. A model of the adsorption/diffusion process is developed to provide a description of the experimental data and shows that, in the case of fluid-phase bilayers, polymerization arises equally due to the adsorption and diffusion of surface-bound monomers and the addition of monomers directly from the solution phase. In contrast, in the case of gel-phase bilayers, polymerization is dominated by the addition of monomers from solution. In both cases, the filaments are stable for long times even when the G-actin is removed from the supernatant—making this a practical approach for creating stable lipid-actin systems via self-assembly

ATTITUDE MANEUVERS OF A FLEXIBLE SPACECRAFT FOR SPACE DEBRIS DETECTION AND COLLISION AVOIDANCE

This work addresses the problem of trajectory and attitude maneuvering of a spacecraft equipped with two flexible solar panels, in response to an alert in two distinct operational scenarios: (a) detection of an approaching debris, and (b) collision avoidance of an impacting debris. In scenario (a) the approaching debris is assumed to be off a collision course with the satellite. As a result, the latter can track the debris, to provide supplementary observations (in addition to those given by ground stations) that allow improving the estimation of its trajectory. Instead, in scenario (b) an impact is predicted, therefore the satellite shall perform a collision avoidance maneuver. This is designed with the objective of minimizing propellant consumption, while ensuring a miss distance greater than a specified threshold value. This research considers the overall dynamics by modeling the spacecraft as a multibody structure, with the use of the Kane's method, which simplifies the process of deriving all the governing equations, while identifying their minimum number. Flexibility is introduced using a modal decomposition technique, under the assumption of small amplitude oscillations. In the two scenarios of interest, efficient strategies are introduced to rotate the solar panels, for the purpose of either maximizing their irradiation or minimizing their oscillations. Attitude maneuvers are driven by two distinct feedback control laws that enjoy quasi-global stability properties. Actuation is modeled as well, by assuming the use of a pyramidal array of four single-gimbal control momentum gyroscopes. Their steering law includes singularity avoidance, based on the singular value decomposition of the actuation matrix. Numerical simulations demonstrate that the agile attitude maneuvering strategies proposed in this study allow achieving the operational objectives in the two scenarios of interest, with limited elastic oscillations