Optimal heading change with minimum energy loss for a hypersonic gliding vehicle
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An overall trajectory for a single-stage-to-orbit vehicle with an initial weight of 234 tons is calculated, and four different propulsion models including turbojet, ramjet, scramjet, and rocket are considered. First, the atmospheric flight in the thicker atmosphere is discussed with emphasis on trajectory optimization, optimization problem, aerodynamic problem, propulsion model, and initial conditions. The performance of turbojet and ramjet-scramjet engines is analyzed; and then the flight to orbit is assessed from the optimization point of view. It is shown that roll modulation saves little during the trajectory, and the combined application of airbreathing propulsion and aerodynamic lift is suggested.
A study was made of the performance of a minimal length cosmic ray shower detector that would be light enough for space flight and would provide efficient identification of positions and protons. Cosmic ray positions are mainly produced in the decay chain of: Pion yields Muon yields Positron and they provide a measure of the matter density traversed by primary protons. Present positron flux measurements are consistent with the Leaky Box and Halo models for sources of cosmic rays. Abundant protons in the space environment are a significant source of background that would wash out the positron signal. Protons and positrons produced very distictive showers of particles when they enter matter; many studies have been published on their behavior on large calorimeter detectors. The challenge is to determine the minimal material necessary (minimal calorimeter depth) for positive particles identification. The primary instrument for the investigation is the Monte Carlo code GEANT, a library of programs from CERN that can be used to model experimental geometry, detector responses and particle interaction processes. The use of the Monte Carlo approach is crucial since statistical fluctuations in shower shape are significant. Studies conducted during the 1988 summer program showed that straightforward approaches to the problem achieved 85 to 90 percent correct identification, but left a residue of 10 to 15 percent misidentified particles. This percentage improved to a few percent when multiple shower-cut criteria were applied to the data. This summer, the same study was extended to employ several physical and statistical methods of identifying response of the calorimeter and the efficiency of the optimal shower cuts to off-normal incidence particle was determined.
The method of moments has found extensive applications in the solution of a wide class of electromagnetic problems. Additionally, there are a number of basis functions which have found favor and with them different types of testing methods. This work examines the selection of test functions, given a selected set of basis functions, which serve to minimize the mean square error. These test functions will guarantee equal or lesser error compared with any other test function. Additionally, these test functions provide a monotonic improvement of the approximation as the increase in the order of the system. Hence while these test functions require the application of the differential or integral operator one additional time, they provide an absolute lower bound to the mean square error in the approximation and a means to systematically improve accuracy with each increase in the order of the unknowns.
Spacecraft reorientation is investigated numerically for an inertially symmetric rigid spacecraft with three bounded independent control torques aligned with the principal axes. The dynamical system of the spacecraft and the framework of the optimal-control problem are established in order to identify all of the potential strategies. The investigation lists bang-bang solutions and finite-order and infinite-order singular arcs, and the conditions for the finite-order singular arcs are given. Numerical examples are developed for all of the control-logic systems, and the suboptimality of the rest-to-rest maneuvers is proven for principal-axis rotations. The most efficient control technique is the singular control of infinite order, and the vector-valued singular control can be utilized in a derivative of the switching function.
The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
Data from a recent APM survey are used to show that large-scale galaxy correlations found there imply the existence of measurable microwave background radiation (MBR) anisotropies on scales greater than several degrees. It is shown that sq rt C(0) is not less than 3.5 x 10 exp -5 if the APM data are used at Theta-0 = 20 deg, or sq rt C(0) is not less than 2.8 x 10 exp -5 if Theta-0 = 10 deg is used. These numbers are almost independent of the cosmological parameters Omega, Lambda, and the redshift of the last scattering surface. For finite-beamwidth experiments the minimal fluctuations depend on the cosmological parameters. The minimal anisotropies are smaller in a low-Omega universe.
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It has been experimentally verified that the jerk of the desired trajectory adversely affects the performance of the tracking control algorithms for robotic manipulators. In this paper, the reasons behind this effect are investigated, and an optimization problem that minimizes joint jerk over a prespecified Cartesian space trajectory is stated. The necessary conditions are derived, and a numerical algorithm is presented.
The motivation was to develop a control design and analysis methodology directly applicable to design concepts of flexible spacecraft of interest the the U.S. Navy and to provide a testbed for the evaluation of large space structure control techniques developed at the Naval Research Laboratory. The topics covered include the following: (1) a list of key concepts; (2) evaluation of the Spacecraft Control Laboratory Experiment (SCOLE) model with DISCOS; (3) baseline results, line of sight error vs. time; (4) general formulation of optimization; (5) geometric interpretation, projected eigenaxis; (6) closed loop control law; and (7) future directions.
Computations were performed to determine the effect of an overall bow-type imperfection on the reliability of structural panels under combined compression and shear loadings. A panel's reliability is the probability that it will perform the intended function - in this case, carry a given load without buckling or exceeding in-plane strain allowables. For a panel loaded in compression, a small initial bow can cause large bending stresses that reduce both the buckling load and the load at which strain allowables are exceeded; hence, the bow reduces the reliability of the panel. In this report, analytical studies on two stiffened panels quantified that effect. The bow is in the shape of a half-sine wave along the length of the panel. The size e of the bow at panel midlength is taken to be the single random variable. Several probability density distributions for e are examined to determine the sensitivity of the reliability to details of the bow statistics. In addition, the effects of quality control are explored with truncated distributions.
In this paper we consider a simple model of real-time scheduling. We present a real-time scheduling system called RTS which is based on Korf's Minimin algorithm. Experimental results show that the schedule quality initially improves with the amount of look-ahead search and tapers off quickly. So it sppears that reasonably good schedules can be produced with a relatively shallow search.
An estimate is found for a lower bound on the Delta V needed for any trajectory which starts at 167 km altitude circular earth orbit and ends in a 100 km altitude circular polar lunar orbit. The analysis used involves calculations of Jacobi's integral in a circular restricted three-body problem which approximates the earth-moon transfer problem. The result is an estimate that any such trajectory will require Delta Vs of at least 3099 km/s to leave the neighborhood of earth and at least 0.622 km/s to achieve the desired orbit around the moon, for a total of 3721 km/s.
The effect produced by the anisotropic gravitational field on the shape of a nonspherical, self-gravitating interstellar cloud is examined. The projected axial ratios observed for molecular clouds can be accounted for if clouds are not generally in a state of strict dynamical equilibrium. For clouds having spectral line widths dominated by supersonic turbulent motions, this purely gravitational effect predicts a mean true axial ratio q about 0.3 for both oblate and prolate cloud geometries. Clouds having p less than about 0.3 are likely to be prolate and quite elongated. The observational data on molecular cloud cores, which have essentially thermal line widths, can be fitted equally well to either oblate or prolate spheroids having q between 0.1 and 0.4 with q about 0.2 providing the best match: highly elongated cores are again more likely to be prolate. While other processes certainly operate throughout the Galaxy to influence cloud shape, it appears plausible that at least some clouds may be shaped principally by their anisotropic gravitational field.
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