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We study Logarithmically Spiral Trajectories and, in particular, we look for a solution to minimize the transit time of a Spacecraft propelled by a Solar Sail, while simultaneously minimizing the area of the Solar Sail, which would allow us to carry more payload on board. We start by analyzing the forces that act on the Spacecraft taking into account that its propellant is a Solar Sail; we use the studied forces to deduce the motion equations. We then solve this motion equation with a Runge-Kutta 4 method and transform the problem of minimizing time and area to a Non-linear Optimization problem. When solving the NLP we also try to minimize the relative final speed of th spacecraft with the destination planet in order to guarantee the possibility of a safe landing on its surface. The model improves when an angle parameter α (describing the angle formed by the Solar Sail with the colliding photons) is defined as a piecewise constant function and optimized whose values are optimized in every interval to minimize transit time and Area. Using the developed model to optimize the trajectory to be followed for sending from Earth to Mars a 2000kg-spacecraft propelled by a Solar Sail, subject to the condition that at trajectory start Mars and Earth were at their closest approach, and the Arrival Relative Velocity is less than 9km/s, give us a minimal transit time of 500days and a minimal area for the Solar Sail of 183158m2, meaning that the maximal payload would be 718kg. Compared with different number of partitions of α, the optimum stays stable. This gives a solid optimal trajectory and a great result for the numerical method used. Actually, waiting until the best moment to throw the Spacecraft, id est, Mars is at 1.14 radians respectively to Earth initial position, the minimal sail area 145950 m2 and, therefore, ables to transport until 978 kg of payload with the same transit time. In addition and to conclude we tried the model to optimize the inverse trajectory.

This template is based on https://github.com/uniba-dsg/dsg-templates/tree/master/dsg-seminar-en You can easily get started by defining variables such as the title of your thesis etc. Chose whether you want the title page with one logo or with two logo. Default is one. Images go in the "images" directory. Other resources, e.g. source code files, go in the "resources" directory. Simply start writing by adding sections in the "sections" directory and including these files in "main.tex". Note, that this template is optimized for theses in computer science with Java as main programming language. But feel free to configure listings, e.g. for other languages.

Estudo de um sistema dinâmico.

Security Insider Lab

Estilos para código fonte para Java e R language!

The minted package provides automatic syntax highlighting for source code listings. It uses the excellent pygments highlighter, which provides very high quality highlighting for a wide range of languages. This example also shows how you can use minted to typeset LaTeX math embedded in your source code.

Template for HCMUT Report

An indoor positioning system relying on time difference of arrival measurements of ultrasonic pings from fixed transmitters. Code available at https://github.com/YingVictor/ultrasonic-positioning

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