Structures in Real Theory Application: A Study in Feasible Epistemology

This thesis considers the following problem: What methods should the epistemology of science use to gain insight into the structure and behaviour of scientific knowledge and method in actual scientific practice? After arguing that the elucidation of epistemological and methodological phenomena in science requires a method that is rooted in formal methods, I consider two alternative methods for epistemology of science. One approach is the classical approaches of the syntactic and semantic views of theories. I show that typical approaches of this sort are inadequate and inaccurate in their representation of scientific knowledge by showing how they fail to account for and misrepresent important epistemological structure and behaviour in science. The other method for epistemology of science I consider is modeled on the methods used to construct valid models of natural phenomena in applied mathematics. This new epistemological method is itself a modeling method that is developed through the detailed consideration of two main examples of theory application in science: double pendulum systems and the modeling of near-Earth objects to compute probability of future Earth impact. I show that not only does this new method accurately represent actual methods used to apply theories in applied mathematics, it also reveals interesting structural and behavioural patterns in the application process and gives insight into what underlies the stability of methods of application. I therefore conclude that for epistemology of science to develop fully as a scientific discipline it must use methods from applied mathematics, not only methods from pure mathematics and metamathematics as traditional formal epistemology of science has done

On the Dynamical Propagation of Subvolumes and on the Geometry and Variational Principles of Nonholonomic Systems.

Their are two main themes of this thesis. The first is the theory and application of the propagation of subvolumes in dynamical systems. We discuss the integral invariants of Poincare-Cartan and introduce a new and closely related set of integral invariants, those of Wirtinger type, and relate these new invariants to a minimum obtainable symplectic volume. We will then consider the application of this approach to the orbit determination and correlation problem for tracking particles of space debris. The second theme is on the geometry of nonholonomic systems. In particular we will focus on the precise geometric understanding of quasi-velocity techniques and its relation to the formulation of variational principles for these systems. We will relate the Euler-Poincar'e equations for Lie groups to the Boltzmann-Hamel equations and further extend both these equations to a higher order form that is applicable to optimal dynamical control problems on manifolds.Ph.D.Applied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58444/1/jmaruski_1.pd

Hadron models and related New Energy issues

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena. The authors explored some new approaches to describe novel phenomena in particle physics. M Pitkanen introduces his nuclear string hypothesis derived from his Topological Geometrodynamics theory, while E. Goldfain discusses a number of nonlinear dynamics methods, including bifurcation, pattern formation (complex GinzburgLandau equation) to describe elementary particle masses. Fu Yuhua discusses a plausible method for prediction of phenomena related to New Energy development. F. Smarandache discusses his unmatter hypothesis, and A. Yefremov et al. discuss Yang-Mills field from Quaternion Space Geometry. Diego Rapoport discusses theoretical link between Torsion fields and Hadronic Mechanic. A.H. Phillips discusses semiconductor nanodevices, while V. and A. Boju discuss Digital Discrete and Combinatorial methods and their likely implications in New Energy research. Pavel Pintr et al. describe planetary orbit distance from modified Schrödinger equation, and M. Pereira discusses his new Hypergeometrical description of Standard Model of elementary particles. The present volume will be suitable for researchers interested in New Energy issues, in particular their link with alternative hadron models and interpretation

Nekhoroshev stability in the elliptic restricted three body problem

Die Frage nach der Langzeitstabilität unseres Sonnensystems kann nach wie vor nicht völlig beantwortet werden. Die Untersuchung dieser Frage hat dennoch, in den letzten Jahrhunderten, die moderne Formulierung heutiger Wissenschaftsdisziplinen maßgeblich beeinflusst (z.B. Hamilton, Lagrange, ...). Bahnbrechende Entdeckungen, wie das KAM und Nekhoroshev Theorem, sind im Umfeld des Spezialgebiets Dynamischer Systeme auf diesem Wege entstanden. Basierend auf Zweiterem, soll in dieser Arbeit gezeigt werden, das es auch um die equilateralen Gleichgewichtspunkte des elliptischen eingeschränkten Dreikörperproblems einen Nekhoroshev-stabilen Bereich gibt, der für das Zeitalter unseres Planetensystems physikalisch relevant ist. Da im Sonnensystem die Massen der Asteroiden im Vergleich zu den Massen der Planeten vernachlässigt werden können folgt aus der Stabilität von Testteilchen im eingeschränkten Dreikörperproblem ebenso die Stabilität von Asteroiden in diesem (in seiner vereinfachten Darstellung). Die Beobachtung von Asteroiden um die Lagrangepunkte, z.B. Jupiters, zusammen mit einer rein mathematischen Theorie, dem Nekhoroshev Theorem, geben Einsicht in die dynamische Entwicklung unseres Sonnensystems. Die vorliegende Studie belegt die Möglichkeit der Langzeit-Stabilität von Asteroiden im Rahmen des elliptisch eingeschränkten Dreikörperproblems. Sie erweitert somit Aussagen vorangegangener Arbeiten, welche auf dem kreisförmigen eingeschränkten Dreikörperproblem basieren. Der Nekhoroshev Bereich im Sonne-Jupiter Fall wurde auf analytischem Wege explizit bestimmt, die stabile Region stimmt bzgl. der Librationsbewegungen mit den Beobachtungen gut überein. Die Stabilität der Trojaner des Sonne-Jupiter Systems konnte für Exzentrizitäten ep<0.01 und Librationsbewegungen Dp<10° für das Zeitalter des Sonnensystems gezeigt werden.The question of the long-term stability of the Solar system is still a partly unsolved problem even nowadays. Nevertheless, the treatment of this problem by various scientists during the last centuries can be seen as the origin of the modern formulation of science, from which i.e. the KAM and the Nekhoroshev theorem originated in the field of dynamical systems. Based on the results of the latter theorem, the goal of the present thesis is to show the existence of a physically relevant Nekhoroshev stable region around the equilateral fixed points of the elliptic restricted 3-body problem for times comparable to the life-time of a planetary system. In the case of our Solar system the masses of the asteroids can be neglected compared to the masses of the planets. A stability result stated in the restricted problem therefore directly translates into a stability result in the Solar system. The observation of asteroids around the Lagrangian equilibrium points on the one hand and the existence of a Nekhoroshev-type stability region around the equilibria on the other hand, validates the assumption. As a conclusion, the observations together with a mathematical theorem gives insight into the dynamical evolution of the Solar system. The present study indicates the possibility of long-term stability of asteroids in the framework of the elliptic restricted three body problem. In the case of Jupiter´s Trojan asteroids, a domain of stability could be derived by analytical means. It is quite realistic with respect to proper librations of the asteroids but limited with respect to the proper eccentricities due to the limited convergence of the series expansion approach. Trojan asteroids in the Sun-Jupiter system are found to be stable for the age of the Solar system for proper eccentricities ep<0.01 and proper librations Dp<10°

Scale relativity and fractal space-time: theory and applications

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to system biology.Comment: 63 pages, 14 figures. In : First International Conference on the Evolution and Development of the Universe,8th - 9th October 2008, Paris, Franc

Publications of the Jet Propulsion Laboratory, 1977

This bibliography cites 900 externally distributed technical reports released during calendar year 1977, that resulted from scientific and engineering work performed, or managed, by the Jet Propulsion Laboratory. Report topics cover 81 subject areas related in some way to the various NASA programs. The publications are indexed by: (1) author, (2) subject, and (3) publication type and number. A descriptive entry appears under the name of each author of each publication; an abstract is included with the entry for the primary (first-listed) author

Publications of the Jet Propulsion Laboratory 1976

The formalized technical reporting, released January through December 1975, that resulted from scientific and engineering work performed, or managed, by the Jet Propulsion Laboratory is described and indexed. The following classes of publications are included: (1) technical reports; (2) technical memorandums; (3) articles from bi-monthly Deep Space Network (DSN) progress report; (4) special publications; and (5) articles published in the open literature. The publications are indexed by: (1) author, (2) subject, and (3) publication type and number. A descriptive entry appears under the name of each author of each publication; an abstract is included with the entry for the primary (first-listed) author. Unless designated otherwise, all publications listed are unclassified

Lunar Crater Identification in Digital Images

It is often necessary to identify a pattern of observed craters in a single image of the lunar surface and without any prior knowledge of the camera's location. This so-called "lost-in-space" crater identification problem is common in both crater-based terrain relative navigation (TRN) and in automatic registration of scientific imagery. Past work on crater identification has largely been based on heuristic schemes, with poor performance outside of a narrowly defined operating regime (e.g., nadir pointing images, small search areas). This work provides the first mathematically rigorous treatment of the general crater identification problem. It is shown when it is (and when it is not) possible to recognize a pattern of elliptical crater rims in an image formed by perspective projection. For the cases when it is possible to recognize a pattern, descriptors are developed using invariant theory that provably capture all of the viewpoint invariant information. These descriptors may be pre-computed for known crater patterns and placed in a searchable index for fast recognition. New techniques are also developed for computing pose from crater rim observations and for evaluating crater rim correspondences. These techniques are demonstrated on both synthetic and real images

Invariant manifolds and transport in a Sun-perturbed Earth-Moon system

[eng] This dissertation is devoted to the analysis of the motion of small bodies, like asteroids, in the neighbourhood of the Earth-Moon system from a celestial mechanics approach. This is an extensive area of research where probably, the most extended simplified mathematical model is the well-known autonomous Hamiltonian system the Restricted Three-Body Problem (RTBP). Many modifications to this model have been proposed, looking for a more accurate description of the system. One of the simplest ways of introducing additional physical effects is through time-periodic perturbations, such that such that the new non-autonomous system is close to the autonomous one, and it has many periodic or quasi-periodic solutions. If these solutions are hyperbolic, they have stable/unstable invariant manifolds, such that stable manifolds approach the quasi-periodic solutions forward in time, meanwhile unstable manifolds do it backward in time, constituting the skeleton for the dynamical transport phenomena we are interested in. Notice that one dimension can be reduced by defining a suitable temporal Poincar´e map. Therefore, our aim is to compute the quasi-periodic solutions and their manifolds in this map. Most of the effort of this dissertation is addressed to the Bicircular Problem (BCP), in which the Earth and Moon are treated as the primaries in the RTBP and the gravitational field of the Sun is introduced as a time-periodic forcing of the RTBP. In particular, we have extensively analysed the horizontal family of two dimensional quasi-periodic solutions in the neighbourhood of the collinear unstable equilibrium point L3. We found that diverse trajectories connecting the Earth, the Moon and the outside Earth-Moon system are governed by L3 dynamics. Big attention is paid to the trajectories coming from the Moon towards the Earth, since they may give an insight of the travel that lunar meteorites perform before landing in our planet. These results have been translated and compared with those of a realistic model based on JPL (Jet Propulsion Laboratory) ephemeris, showing a good agreement between the results obtained. We also have proposed and carried out a strategy for capturing a Near Earth Asteroid (NEA) using the stable invariant manifolds of the horizontal family of quasi-periodic orbits around L3 in the BCP. To this aim the high order parametrization of the stable/unstable invariant manifolds is introduced, for which computation we have employed the jet transport technique. Finally, the strategy is applied to the NEA 2006 RH120. The contributions to the BCP presented in this dissertation include two other applications. The first one is devoted to the study of the unstable behaviour near the triangular points, meanwhile the second is devoted to a family of stable invariant curves around the Moon that are close to a resonance, promoting the appearance of chaotic motion. The last part of the dissertation is focused on the effective computation of the high or- der parametrization of the stable and unstable invariant manifolds associated with reducible invariant tori of any high dimension. To this aim, we resort on the reducible system, that offers a high degree of parallelization of the computations. Besides, we explain how to com- bine the presented methods with multiple shooting techniques to accurately compute highly unstable invariant objects. Finally, we apply the developed algorithms to compute the high order parametrization of the manifolds associated to L1 and L2 in an Earth-Moon system that includes five time-periodic forcings regarded to four physical features of the system, besides the solar gravitational field.[spa] Esta tesis analiza el movimiento de pequeños cuerpos, como asteroides, en el sistema Tierra­ Luna desde el marco de la mecánica celeste. El modelo que hemos empleado en mayor profundidad es el Problema Bicircular (PBC), el cual se puede entender como una perturbación periódica en el tiempo del conocido Problema Restringido de Tres Cuerpos (PRTC), dado que en el PBC se incluye el campo gravitatorio de un tercer cuerpo masivo que rota en movimiento circular alrededor de la configuración del PRTC. El cuerpo que causa la perturbación es para nosotros el Sol de tal forma que los objetos invariantes del PRTC adquieren una dimensión angular debida a la frecuencia del movimiento relativo entre el Sol y el baricentro Tierra-Luna. En el marco del PBC hemos analizado los fenómenos de transporte gobernados por la familia horizontal de soluciones cuasi-periódicas dos dimensionales (toros 2D) alrededor punto inestable colinear L3. Estas soluciones tienen asociadas variedades invariantes estables e inestables que constituyen el esqueleto de los fenómenos que queremos estudiar. Las trayectorias encontradas conectan la Tierra y la Luna y también el exterior/interior del sistema Tierra-Luna. Hemos prestado especial atención a las trayectorias que van de la Luna a la Tierra ya que podrían explicar el viaje que realizan los meteoritos lunares encontrados en nuestro planeta. Estos resultados han sido testeados en un modelo más realista basado en las efemérides del JPL (Jet Propulsion Laboratory). Otra de las aplicaciones propuestas es la de capturar un asteroide cercano a la Tierra usando la parametrización a orden alto de las variedades invariantes asociadas a los toros 2D alrededor de L3. La parte final trata del desarrollo de algoritmos para el cálculo preciso de la parametrización a orden alto de variedades invariantes estables/inestables asociadas a toros reducibles de cualquier dimensión alta. Además, se explica cómo combinar dichos algoritmos con métodos de tiro múltiple para aquellos objetos invariantes que sean muy inestables. Finalmente, aplicamos la metodología al cálculo de las variedades asociadas a L1 y L2 de un sistema Tierra-Luna que incluye cinco perturbaciones periódicas en el tiempo