An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

Differenzielles Lehren und Lernen: eine Kritik

Dieser Beitrag beschäftigt sich kritisch mit dem von Wolfgang Schöllhorn seit 1999 propagierten Ansatz des differenziellen Lehrens und Lernens. Nach einer Einordnung in die historische bewegungswissenschaftliche Debatte um den Informationsverarbeitungsansatz und die dynamische Systemtheorie zeigen wir, dass die von Schöllhorn behaupteten Praxiskonsequenzen theoretisch nicht fundiert sind, dass die Abgrenzung zu konkurrierenden Lerntheorien lücken- und fehlerhaft ausfällt, dass die präsentierte empirische Befundlage auf höchst wackeligen Füßen steht und dass der Ansatz sich auch aus Praxissicht als nicht tragfähig erweist. Mit Blick auf fatale Konsequenzen sowohl für die Sportpraxis als auch für die Sportwissenschaft empfehlen wir, in zukünftigen Publikationen zum differenziellen Lernen auf fehlerhafte und theoretisch wie empirisch unbegründete Praxisempfehlungen zu verzichten.

Capability of a space-based space surveillance system to detect and track objects in GEO, MEO and LEO orbits

In this paper we present the results from the coverage and the orbit determination accuracy simulations performed within the recently completed ESA study “Assessment Study for Space Based Space Surveillance (SBSS) Demonstration System” (Airbus Defence and Space consortium). This study consisted in investigating the capability of a space based optical sensor (SBSS) orbiting in low Earth orbit (LEO) to detect and track objects in GEO (geosynchronous orbit), MEO (medium Earth orbit) and LEO and to determinate and improve initial orbits from such observations. Space based systems may achieve better observation conditions than ground based sensors in terms of astrometric accuracy, detection coverage, and timeliness. The primary observation mode of the proposed SBSS demonstrator is GEO surveillance, i.e. the systematic search and detection of unknown and known objects. GEO orbits are specific and unique orbits from dynamical point of view. A space-based sensor may scan the whole GEO ring within one sidereal day if the orbit and pointing directions are chosen properly. For an efficient survey, our goal was to develop a leak-proof GEO fence strategy. Collaterally, we show that also MEO, LEO and other (GTO,Molniya, etc.) objects would be possible to observe by the system and for a considerable number of LEO objects to down to size of 1 cm we can obtain meaningful statistical data for improvement and validation of space debris environment models

All-sky Meteor Orbit System AMOS and preliminary analysis of three unusual meteor showers

All-sky Meteor Orbit System (AMOS) is a semi-autonomous video observatory for detection of transient events on the sky, mostly the meteors. Its hardware and software development and permanent placement on several locations in Slovakia allowed the establishment of Slovak Video Meteor Network (SVMN) monitoring meteor activity above the Central Europe. The data reduction, orbital determination and additional results from AMOS cameras–the SVMN database– as well as from observational expeditions on Canary Islands and in Canada provided dynamical and physical data for better understanding of mutual connections between parent bodies of asteroids and comets and their meteoroid streams. We present preliminary results on exceptional and rare meteor streams such as September ε Perseids (SPE) originated from unknown long periodic comet on a retrograde orbit, suspected asteroidal meteor stream of April α Comae Berenicids (ACO) in the orbit of meteorites Příbram and Neuschwanstein and newly observed meteor stream Camelopardalids (CAM) originated from Jupiter family comet 209P/Linear.

Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.