Some effects of digital sampling on orbiter flight control system operation

An entry dynamic stability ground test of the OV102 Space Shuttle Orbiter revealed some small amplitude oscillatory output of the flight control system which could have constrained flight of the STS-1 mission. These limit-cycle-type outputs were attributed to a combination of rigid body motion of the Orbiter on its landing gear and some interesting effects of its digital flight control system. These effects included frequency aliasing and phenomena associated with digital quantitization of low amplitude sensor signals. The digital effects suggest significant improvements possible in future designs

How terrestrial planets traverse spin-orbit resonances: A camel goes through a needle's eye

The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love numbers. The torque equations are integrated numerically with a small step in time, includng the oscillating triaxial torque components but neglecting the layered structure of the planet and assuming a zero obliquity. We find that a Mercury-like planet with its current value of orbital eccentricity (0.2056) is always captured in the 3:2 resonance. The probability of capture in the higher 2:1 resonance is approximately 0.23. These results are confirmed by a semi-analytical estimation of capture probabilities as functions of eccentricity for both prograde and retrograde evolution of spin rate. As follows from analysis of equilibrium torques, entrapment in the 3:2 resonance is inevitable at eccentricities between 0.2 and 0.41. Considering the phase space parameters at the times of periastron, the range of spin rates and phase angles, for which an immediate resonance passage is triggered, is very narrow, and yet, a planet like Mercury rarely fails to align itself into this state of unstable equilibrium before it traverses the 2:1 resonance.Comment: 10 figures. Fig. 8 may be corrupted when printed on some printers but shows fine in the PDF file. Submitted in ApJ v. 2: the probabilities of capture of Mercury in 2:1 resonance are re-evaluated; a general formula for capture probability derived. v3: accepted in ApJ under a different title: Conditions of passage and entrapment of terrestrial planets in spin-orbit resonance

Robot docking using mixtures of Gaussians

This paper applies the Mixture of Gaussians probabilistic model, combined with Expectation Maximization optimization to the task of summarizing three dimensionals range data for the mobile robot. This provides a flexible way of dealing with uncertainties in sensor information, and allows the introduction of prior knowledge into low-level perception modules. Problems with the basic approach were solved in several ways: the mixture of Gaussians was reparameterized to reflect the types of objects expected in the scene, and priors on model parameters were included in the optimization process. Both approaches force the optimization to find 'interesting' objects, given the sensor and object characteristics. A higher level classifier was used to interpret the results provided by the model, and to reject spurious solutions

Generalized Hamilton-Jacobi equations for nonholonomic dynamics

Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the action is actually minimized (not just extremized)

Relationships Between Classroom Schedule Types and Performance on the Algebra I Criterion-Referenced Test

Public education has options with regard to educational settings and structures. States and school districts may select varying lengths for the school year, lengths for the school day, and lengths for individual class periods. In Utah, one measure of students\u27 achievement is scores on the State\u27s end-of-level criterion-referenced test (CRT) for Algebra I. Additionally, an option regarding educational structures is the schedule type used to deliver Algebra I classes. This study examined the relationship between student achievement as measured by Algebra I CRT scores, and the schedule type used to deliver Algebra I classes. The schedule types compared were the traditional daily schedule, trimester 3/3 schedule, trimester 2/3 schedule, and the block A/B schedule. This study sought to answer two research questions: (1) What is the relationship between mathematics instructional schedule type and student scores on Utah\u27s CRT for Algebra I, for all students? and (2) What is the relationship between mathematics instructional schedule type and student scores on Utah\u27s CRT for Algebra I, by individual grade levels? Data were obtained from the Utah State Office of Education and included the scores for 50,000 Utah students, from over 300 different schools, who took the identical Algebra I CRT at the end of the 2010-2011 school year. Data were also obtained from each school district to determine the schedule type of each participating student. Both a multinomial logistic regression analysis and a t-test analysis were conducted to determine relationships between Algebra I CRT scores and schedule types. The results indicated significant differences in student achievement based on the schedule type overall and for individual grade levels. Generally, the earlier the grade level the higher the CRT score. Within individual grade levels, there were both statistically significant and nonsignificant differences. The schedule types that generally score the highest (trimester 3/3 and traditional) had more time in the mathematics classroom and the students\u27 mathematics class met daily. The results suggest the value of daily time spent in the mathematics classroom and may assist educators when considering options available to foster student achievement