Lagrangian multipliers for coast-arcs of optimum space trajectories

Some properties of generalized canonical systems - special dynamical systems described by a Hamiltonian function linear in the adjoint variables - are applied in determining the solution of the two-dimensional coast-arc problem in an inverse-square gravity field. A complete closed-form solution for Lagrangian multipliers - adjoint variables - is obtained by means of such properties for elliptic, circular, parabolic and hyperbolic motions. Classic orbital elements are taken as constants of integration of this solution in the case of elliptic, parabolic and hyperbolic motions. For circular motion, a set of nonsingular orbital elements is introduced as constants of integration in order to eliminate the singularity of the solution.

Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.

Global trajectory optimisation: can we prune the solution space when considering deep space manoeuvres?

This document contains a report on the work done under the ESA/Ariadna study 06/4101 on the global optimization of space trajectories with multiple gravity assist (GA) and deep space manoeuvres (DSM). The study was performed by a joint team of scientists from the University of Reading and the University of Glasgow.

Earth-Venus trajectories.

Includes bibliographies.

Diffusive Synchronization of Hyperchaotic Lorenz Systems

The synchronizing properties of two diffusively coupled hyperchaotic Lorenz 4D systems are investigated by calculating the transverse Lyapunov exponents and by observing the phase space trajectories near the synchronization hyperplane. The effect of parameter mismatch is also observed. A simple electrical circuit described by the Lorenz 4D equations is proposed. Some results from laboratory experiments with two coupled circuits are presented. Copyright (C) 2009 Ruy Barboza.

Inherently self-calibrating non-Cartesian parallel imaging.

The use of self-calibrating techniques in parallel magnetic resonance imaging eliminates the need for coil sensitivity calibration scans and avoids potential mismatches between calibration scans and subsequent accelerated acquisitions (e.g., as a result of patient motion). Most examples of self-calibrating Cartesian parallel imaging techniques have required the use of modified k-space trajectories that are densely sampled at the center and more sparsely sampled in the periphery. However, spiral and radial trajectories offer inherent self-calibrating characteristics because of their densely sampled center. At no additional cost in acquisition time and with no modification in scanning protocols, in vivo coil sensitivity maps may be extracted from the densely sampled central region of k-space. This work demonstrates the feasibility of self-calibrated spiral and radial parallel imaging using a previously described iterative non-Cartesian sensitivity encoding algorithm.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

Clustering and diffusion in a symplectic map lattice with non-local coupling

We study a symplectic chain with a non-local form of coupling by means of a standard map lattice where the interaction strength decreases with the lattice distance as a power-law, in Such a way that one can pass continuously from a local (nearest-neighbor) to a global (mean-field) type of coupling. We investigate the formation of map clusters, or spatially coherent structures generated by the system dynamics. Such clusters are found to be related to stickiness of chaotic phase-space trajectories near periodic island remnants, and also to the behavior of the diffusion coefficient. An approximate two-dimensional map is derived to explain some of the features of this connection. (C) 2008 Elsevier Ltd. All rights reserved.

Sub-Optimal Orbital Maneuvers for Artificial Satellites

The determination of a specific orbit and the procedure to calculate orbital maneuvers of artificial satellites are problems of extreme importance in the study of orbital mechanics. Therefore, the transferring problem of a spaceship from one orbit to another, and the attention due to this subject has in increased during the last years. Many applications can be found in several space activities, for example, to put a satellite in a geostationary orbit, to change the position of a spaceship, to maintain a specific satellite's orbit, in the design of an interplanetary mission, and others. The Brazilian Satellite SCD-1 (Data Collecting Satellite) will be used as example in this paper. It is the first satellite developed entirely in Brazil, and it remains in operation to this date. SCD-1 was designed, developed, built, and tested by Brazilian scientists, engineers, and technicians working at INPE (National Institute for Space Research, and in Brazilian Industries. During the lifetime, it might be necessary do some complementary maneuvers, being this one either an orbital transferring, or just to make periodical corrections. The purpose of transferring problem is to change the position, velocity and the satellite's mass to a new pre determined state. This transfer can be totally linked (in the case of "Rendezvous") or partially free (free time, free final velocity, etc). In the global case, the direction, the orientation and the magnitude of the thrust to be applied must be chosen, respecting the equipment's limit. In order to make this transferring, either sub-optimal or optimal maneuvers may be used. In the present study, only the sub-optimal will be shown. Hence, this method will simplify the direction of thrust application, to allow a fast calculation that may be used in real time, with a very fast processing. The thrust application direction to be applied will be assumed small and constant, and the purpose of this paper is to find the time interval that the thrust is applied. This paper is basically divided into three parts: during the first one the sub-optimal maneuver is explained and detailed, the second presents the Satellite SCD-1, and finally the last part shows the results using the sub-optimal maneuver applied to the Brazilian Satellite.

Event-related potential P300 microstate topography during visual one- and two-dimensional tasks in chronic schizophrenics

Reports on left-lateralized abnormalities of component P300 of event-related brain potentials (ERP) in schizophrenics typically did not vary task difficulties. We collected 16-channel ERP in 13 chronic, medicated schizophrenics (25±4.9 years) and 13 matched controls in a visual P300 paradigm with targets defined by one or two stimulus dimensions (C1: color; C2: color and tilt); subjects key-pressed to targets. The mean target-ERP map landscapes were assessed numerically by the locations of the positive and negative map-area centroids. The centroids' time-space trajectories were searched for the P300 microstate landscape defined by the positive centroid posterior of the negative centroid. At P300 microstate centre latencies in C1, patients' maps tended to a right shift of the positive centroid (p<0.10); in C2 the anterior centroid was more posterior (p<0.07) and the posterior (positive) centroid more anterior (p<0.03), but without leftright difference. Duration of P300 microstate in C2 was shorter in patients (232 vs 347 ms;p<0.03) and the latency of maximal strength of P300 microstate increased significantly in patients (C1: 459 vs 376 ms; C2: 585 vs 525 ms). In summary only the one-dimensional task C1 supported left-sided abnormalities; the two-dimensional task C2 produced abnormal P300 microstate map landscapes in schizophrenics, but no abnormal lateralization. Thus, information processing involved clearly aberrant neural populations in schizophrenics, different when processing one and two stimulus dimensions. The lack of lateralization in the two-dimensional task supported the view that left-temporal abnormality in schizophrenics is only one of several task-dependent aberrations.

Analysis of missile trajectory measurement accuracy for data processing

"Contract no. AF 30(602)-2138, Project 5554, Task 55102."

Dispersal of reactor core materials by reentry processes; preliminary analysis,

"Project no. AA-1506-W. Contract no. P.O. no.51-1136. Sub order no. 7, Sandia Corporation."

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.

Search space pruning and global optimisation of Multiple Gravity Assist spacecraft trajectories

We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation.