Basins of attraction in nonsmooth models of gear rattle

This paper is concerned with the computation of the basins of attraction of a simple one degree-of-freedom backlash oscillator using cell-to-cell mapping techniques. This analysis is motivated by the modeling of order vibration in geared systems. We consider both a piecewise-linear stiffness model and a simpler infinite stiffness impacting limit. The basins reveal rich and delicate dynamics, and we analyze some of the transitions in the system's behavior in terms of smooth and discontinuity-induced bifurcations. The stretching and folding of phase space are illustrated via computations of the grazing curve, and its preimages, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit)

Improvements to Integrated Tradespace Analysis of Communications Architectures (ITACA) Network Loading Analysis Tool

NASA's SCENIC project aims to simplify and reduce the cost of space mission planning by replicating the analysis capabilities of commercially licensed software which are integrated with relevant analysis parameters specific to SCaN assets and SCaN supported user missions. SCENIC differs from current tools that perform similar analyses in that it 1) does not require any licensing fees, 2) will provide an all-in-one package for various analysis capabilities that normally requires add-ons or multiple tools to complete. As part of SCENIC's capabilities, the ITACA network loading analysis tool will be responsible for assessing the loading on a given network architecture and generating a network service schedule. ITACA will allow users to evaluate the quality of service of a given network architecture and determine whether or not the architecture will satisfy the mission's requirements. ITACA is currently under development, and the following improvements were made during the fall of 2017: optimization of runtime, augmentation of network asset pre-service configuration time, augmentation of Brent's method of root finding, augmentation of network asset FOV restrictions, augmentation of mission lifetimes, and the integration of a SCaN link budget calculation tool. The improvements resulted in (a) 25% reduction in runtime, (b) more accurate contact window predictions when compared to STK(Registered Trademark) contact window predictions, and (c) increased fidelity through the use of specific SCaN asset parameters

Distributed Location Estimation of a Moving Target Characterized by a Spatial Poisson Field

Wireless Sensor Networks (WSNs) are traditionally employed to collect spatial and temporal data characterizing various events. These data are then used to solve inference problems such as object detection, counting, classification, estimation and tracking. Distributed solutions provided by WSNs are often cost effective and characterized by high performance indices.;In this work, we model and simulate a distributed sensor network composed of radiation detectors and analyze its ability to make inferences. Radiation detectors are deployed over a known area. A radiological point source is positioned in the interior of the area. Detectors take measurements of the field generated by the point source and transmit them (without any interaction with one another) to a remotely installed super computer (called here Fusion Center) for a joint processing. To minimize consumption of resources such as power in the network and transmission bandwidth, the measurements are locally preprocessed prior to transmission. Our model assumes two Gaussian channels, observation and transmission. The first channel distorts data at the receiver end of each sensor during data acquisition. The second channel distorts data during transmission. Sensor measurements are modeled as an inhomogeneous spatial counting random process (Poisson process). The location of the radiological point source in the area and the strength of the field generated by the substance are unknown parameters. The goal of the FC is to estimate these parameters from the distributed measurements provided by the WSN. To find the distributed estimates, we adopt the Maximum Likelihood approach. This approach requires knowledge of the joint probability density function of the distributed measurements observed by the FC. Since the joint probability density of the data observed at the FC is nonlinear in unknown parameters, we propose an iterative approach to solve for the maximum likelihood estimates of these parameters. The solution is a combination of the Bisection and Secant approaches adjusted to seek solution in a multidimensional parameter space. The performance of the distributed estimator is measured in terms of the mean square error. It is analyzed with respect to various parameters of the WSN. We vary the following parameters of the network: (1) the number of sensors in the WSN, (2) signal to noise ratio in observation and transmission channels, (3) the strength of the original field, and (4) the number of quantization levels used by a sensor to convert an analog measurement into a digital signal. We also propose a distributed tracking algorithm for monitoring position of the object in real time

Parameter estimation supplement to the Mission Analysis Evaluation and Space Trajectory Operations program (MAESTRO)

This Parameter Estimation Supplement describes the PEST computer program and gives instructions for its use in determination of lunar gravitation field coefficients. PEST was developed for use in the RAE-B lunar orbiting mission as a means of lunar field recovery. The observations processed by PEST are short-arc osculating orbital elements. These observations are the end product of an orbit determination process obtained with another program. PEST's end product it a set of harmonic coefficients to be used in long-term prediction of the lunar orbit. PEST employs some novel techniques in its estimation process, notably a square batch estimator and linear variational equations in the orbital elements (both osculating and mean) for measurement sensitivities. The program's capabilities are described, and operating instructions and input/output examples are given. PEST utilizes MAESTRO routines for its trajectory propagation. PEST's program structure and subroutines which are not common to MAESTRO are described. Some of the theoretical background information for the estimation process, and a derivation of linear variational equations for the Method 7 elements are included

A two-species continuum model for aeolian sand transport

Starting from the physics on the grain scale, we develop a simple continuum description of aeolian sand transport. Beyond popular mean-field models, but without sacrificing their computational efficiency, it accounts for both dominant grain populations, hopping (or "saltating") and creeping (or "reptating") grains. The predicted stationary sand transport rate is in excellent agreement with wind tunnel experiments simulating wind conditions ranging from the onset of saltation to storms. Our closed set of equations thus provides an analytically tractable, numerically precise, and computationally efficient starting point for applications addressing a wealth of phenomena from dune formation to dust emission.Comment: 23 pages, 9 figure

Comparative analysis of polynomial root finding techniques

The purpose of this study was to investigate and recommend various methods instrumental in finding the roots of a polynomial p(x) = 0. Many different methods are present today, and each has its advantages and disadvantages. Through thorough investigation, the author has ascertained the key methods to be the method of Bisection, the Newton-Raphson method, and the Bairstow method. Special support in the form of algebraic theorems on the locations and kind of roots are extremely helpful. This combination of theorems and methods provides assurance, speed, and the ability to obtain complex roots. The Bisnewbar method developed by this author combines the above methods and the algebraic theorems to provide a method capable of returning all real and complex roots --Abstract, page i