Understanding the Hamiltonian Function through the Geometry of Partial Legendre Transforms

The relationship between the Hamiltonian and Lagrangean functions in analytical mechanics is a type of duality. The two functions, while distinct, are both descriptive functions encoding the behavior of the same dynamical system. One difference is that the Lagrangean naturally appears as one investigates the fundamental equation of classical dynamics. It is not that way for the Hamiltonian. The Hamiltonian comes after Lagrange's equations have been fully formed, most commonly through a Legendre transform of the Lagrangean function. We revisit the Legendre transform approach and offer a more refined geometrical interpretation than what is commonly shown

An O(n log n)-Time Algorithm for the Restricted Scaffold Assignment

The assignment problem takes as input two finite point sets S and T and establishes a correspondence between points in S and points in T, such that each point in S maps to exactly one point in T, and each point in T maps to at least one point in S. In this paper we show that this problem has an O(n log n)-time solution, provided that the points in S and T are restricted to lie on a line (linear time, if S and T are presorted).Comment: 13 pages, 8 figure

Pattern Recognition for a Flight Dynamics Monte Carlo Simulation

The design, analysis, and verification and validation of a spacecraft relies heavily on Monte Carlo simulations. Modern computational techniques are able to generate large amounts of Monte Carlo data but flight dynamics engineers lack the time and resources to analyze it all. The growing amounts of data combined with the diminished available time of engineers motivates the need to automate the analysis process. Pattern recognition algorithms are an innovative way of analyzing flight dynamics data efficiently. They can search large data sets for specific patterns and highlight critical variables so analysts can focus their analysis efforts. This work combines a few tractable pattern recognition algorithms with basic flight dynamics concepts to build a practical analysis tool for Monte Carlo simulations. Current results show that this tool can quickly and automatically identify individual design parameters, and most importantly, specific combinations of parameters that should be avoided in order to prevent specific system failures. The current version uses a kernel density estimation algorithm and a sequential feature selection algorithm combined with a k-nearest neighbor classifier to find and rank important design parameters. This provides an increased level of confidence in the analysis and saves a significant amount of time

Transmisión de información usando la modulación (DSSS) espectro ensanchado por secuencia directa

Dada la creciente evolución en el mundo de la electrónica y en específico del campo enfatizado en esta investigación, las telecomunicaciones, es importante que la formación como ingenieros se encuentre en un proceso de actualización y de aprendizaje constantes, con miras hacia el desarrollo de nuevas tecnologías, en este caso Spread Spectrum. Esta técnica en sus inicios era una tecnología que por su complejidad y altos costos era de uso exclusivo para proyectos militares, siendo difícil acceder a ella para utilizarla en aplicaciones comerciales; la integración a gran escala de circuitos digitales permitió colocar el costo de la tecnología de "Spread Spectrum" en un nivel realista para desarrollar aplicaciones comerciales. En este proyecto se hace uso de la técnica antes mencionada para implementarla en un circuito integrado de gran auge comercial como lo es la FPGA1, que por su naturaleza y funcionamiento es la ideal para emular circuitos físicos tales como compuertas lógicas, multiplexores, moduladores y demoduladores, etc. La finalidad de este proyecto es desarrollar un sistema de comunicación aplicando los principios de la técnica Spread Spectrum, para así comprobar y verificar su correcto desempeño sobre un dispositivo de hardware reconfigurable (FPGA), dicha comunicación entre modulador y demodulador se realizará mediante un par de cobre, así se determinará la viabilidad de utilizar dicho principio en el intercambio de información

Identificación y detección de fallas en accionamiento utilizando NN-NARX

In this paper, the use of a Nonlinear Auto Regressive eXogenous Neural Networks model or NN-NARX for identification and fault detection in the actuator of an industrial thermal process is presented. Initially, the techniques of fault detection and diagnosis are exposed; then, emphasis is placed on the models of Artificial Neural Networks for identification and fault detection. Subsequently, the control system of a thermal process used as a case study is described. A monitoring system allows data recording under normal operation conditions for identification using the NN-NARX model. The model is used for residual online generation due to faults that are introduced randomly. Finally, the results of residual generation and evaluation are presented. The designed system is useful for implementation through a hardware device that can be incorporated into the process equipment and support the operator in the presence of failures.En este artículo se presenta la utilización de un modelo de Red Neuronal no lineal Auto Regresivo de Variable Exógena o NN-NARX (por sus siglas en inglés), para la identificación y detección de fallas en un accionamiento de un proceso térmico industrial. Inicialmente, se exponen las técnicas de detección y diagnóstico de fallas; luego, se hace énfasis en los modelos de Redes Neuronales Artificiales para identificación y detección de fallas. Posteriormente, se describe el sistema de control de un proceso térmico utilizado como caso de estudio. Un sistema de monitorización permite el registro de datos en condiciones normales de operación para la identificación usando el modelo NN-NARX. El modelo es utilizado para la generación en línea de residuos ante fallas que son introducidas aleatoriamente. Finalmente, se presentan los resultados de la generación y evaluación de residuos. El sistema diseñado es útil para la implementación a través de un dispositivo hardware que puede incorporarse en el equipo del proceso y apoyar al operador ante la presencia de fallas

Tool for Rapid Analysis of Monte Carlo Simulations

Designing a spacecraft, or any other complex engineering system, requires extensive simulation and analysis work. Oftentimes, the large amounts of simulation data generated are very di cult and time consuming to analyze, with the added risk of overlooking potentially critical problems in the design. The authors have developed a generic data analysis tool that can quickly sort through large data sets and point an analyst to the areas in the data set that cause specific types of failures. The Tool for Rapid Analysis of Monte Carlo simulations (TRAM) has been used in recent design and analysis work for the Orion vehicle, greatly decreasing the time it takes to evaluate performance requirements. A previous version of this tool was developed to automatically identify driving design variables in Monte Carlo data sets. This paper describes a new, parallel version, of TRAM implemented on a graphical processing unit, and presents analysis results for NASA's Orion Monte Carlo data to demonstrate its capabilities