Transfer orbits to/from the Lagrangian points in the restricted four-body problem

The well-known Lagrangian points that appear in the planar restricted three-body problem are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L₁, L₂ and L₃) are always unstable and the triangular points (L₄ and L₅) are stable in the present case studied (Earth–Sun system). They are all very good points to locate a space-station, since they require a small amount of ΔV (and fuel), the control to be used, for station-keeping. The triangular points are especially good for this purpose, since they are stable equilibrium points.In this paper, the planar restricted four-body problem applied to the Sun–Earth–Moon–Spacecraft is combined with numerical integration and gradient methods to solve the two-point boundary value problem. This combination is applied to the search of families of transfer orbits between the Lagrangian points and the Earth, in the Earth–Sun system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the Lagrangian point and the second one when arriving/living at the Earth.The dynamics given by the restricted four-body problem is used to obtain the trajectory of the spacecraft, but not the position of the equilibrium points. Their position is taken from the restricted three-body model. The goal to use this model is to evaluate the perturbation of the Sun in those important trajectories, in terms of fuel consumption and time of flight. The solutions will also show how to apply the impulses to accomplish the transfers under this force model.The results showed a large collection of transfers, and that there are initial conditions (position of the Sun with respect to the other bodies) where the force of the Sun can be used to reduce the cost of the transfers.     

The knowledge of knots: an interdisciplinary literature review

ABSTRACT

Knots can be found and used in a variety of situations in the 3D world, such as in vines, in the DNA, polymer chains, electrical wires, in mountaineering, seamanship and when ropes or other flexible objects are involved for exerting forces and holding objects in place. Research on knots as topological entities has contributed with a number of findings, not only of interest to pure mathematics, but also to statistical mechanics, quantum physics, genetics, and chemistry. Yet, the cognitive (or algorithmic) aspects involved in the act of tying a knot are a largely uncharted territory. This paper presents a review of the literature related to the investigation of knots from the topological, physical, cognitive and computational (including robotics) standpoints, aiming at bridging the gap between pure mathematical work on knot theory and macroscopic physical knots, with an eye to applications and modeling.     

The GANDER constellation for maritime dissaster mitigation

The development of sea state monitoring from polar-orbiting satellites has recently moved away from the concept of single, multi-sensor platform such as ERS-2, Topex/Poseidon or ENVISAT towards the design of a system that would allow frequent updates from a constellation of small satellites equipped with special-purpose radar altimeters. This new system, called GANDER for Global Altimeter Network Designed to Evaluate Risk, has attracted significant support from a number of important customer segments including the military.

This paper details the design of an altimeter for a Surrey small satellite, and illustrates the major system trade-offs that need to be made. Critical to the viability of the mission will be the development of a radar altimeter capable of operating successfully on a small satellite bus, within a limited volume and power budget. The mission design presents a number of key technological challenges, in order to permit a physically small antenna to be employed, and to minimise the pulse power. This can be achieved by advanced techniques, such as the delay Doppler altimeter concept, which emphasises the needs for high-speed on-board signal processing, phase linearity and pulse-to-pulse phase coherency.

The system design for the GANDER constellation is also described, illustrating how it not only offers a means for maritime disaster mitigation, but also can reduce shipping cost and time.     

HW/SW Co-design of the Instrument Control Unit for the Energetic Particle Detector on-board Solar Orbiter

ESA’s medium-class Solar Orbiter mission is conceived to perform a close-up study of our Sun and its inner heliosphere to better understand the behaviour of our star. The mission will provide the clues to discover how the Sun creates and controls the solar wind and thereby affects the environments of all the planets. The spacecraft is equipped with a comprehensive suite of instruments. The Energetic Particle Detector (EPD) is one of the in-situ instruments on-board Solar Orbiter. EPD is composed of five different sensors, all of them sharing the Instrument Control Unit or ICU that is the sole interface with the spacecraft. This paper emphasises on how the hardware/software co-design approach can lead to a decrease in software complexity and highlights the versatility of the toolset that supports the development process. Following a model-driven engineering approach, these tools are capable of generating the high-level code of the software application, as well as of facilitating its configuration control and its deployment on the hardware platforms used in the different stages of the development process. Moreover, the use of the Leon2ViP virtual platform, with fault injection capabilities, allows an early software-before-hardware verification and validation and also a hardware–software co-simulation. The adopted solutions reduce development time without compromising the whole process reliability that is essential to the EPD success.     

一种用于深空通信的系统LT码

针对传统LT（Luby Transform）码用于深空通信时性能不理想的问题,通过重构LT码的二分图设计适用于深空通信环境的系统LT码,提出一种去环编码算法。采用外信息转移图分析系统LT码的收敛阈值,然后通过仿真试验评估系统LT码的性能。仿真结果表明,采用本文提出的编码方案的系统LT码能够明显降低错误平层,提高译码算法的性能。