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Rotation vector in attitude estimation

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2003年第6期26卷 855-860页

作者： Pittelkau, ME Johns Hopkins Univ Appl Phys Lab Laurel MD 20723 USA

An alternative derivation of the spacecraft attitude determination filter is developed to avoid questions of quaternion normalization or attitude matrix orthogonality constraints, quaternion covariance, and subterfuges used to circumvent these problems. This derivation is based on the Bortz equation for the rotation vector. Because the rotation vector is an unconstrained representation of attitude, the aforementioned questions do not arise. Singularities in the state dynamics equation are avoided by maintaining the predicted body attitude as the inertial reference for the filter. A simple discrete solution to the Bortz equation provides accurate attitude propagation for highly maneuverable spacecraft and also in. the presence of jitter.

关键词： Quaternions Maneuverable Spacecraft Spacecraft Attitude White Noise Three Axis Magnetometer integration algorithm Body Reference Frame Euler Angles Aircraft Navigation Systems Dirac Delta Function

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Inverse dynamics of aircraft via reduced-order shooting methods

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2002年第6期25卷 1158-1162页

作者： Bernelli-Zazzera, F Cappello, G Mantegazza, P Politecn Milan Dept Aerosp Engn I-20158 Milan Italy

The inverse simulation of a military trainer aircraft is treated. The inverse simulation problem requires the determination of control inputs that will make a set of specified states follow a prescribed trajectory. The method proposed here allows an arbitrary combination of very general path and dynamics constraints, and, at the same time, it optimizes a defined performance index. The method departs from the classical approach for trajectory optimization based on direct transcription. It arises from the concept of combining collocation and direct transcription and has the advantage of minimizing the number of variables and constraints involved in the numerical optimization with special regard to the equality constraints deriving from the direct transcription. This minimization of constraints and variables allowed the study of the inverse problem of the aircraft, including the dynamics of the actuators, on a personal computer, in a reasonable time, and without the need of using any specialized sparse optimization tool. It has been shown that the use of direct methods avoids both the explicit specification of, and the analytical conditions for, the Lagrange multipliers and the analytical differentiation of constraints on the path and on the state, thus making it simpler to use tabulated aeromechanics databases. (Author)

关键词： Trainer Aircraft Numerical Optimization Trajectory Optimization Mathematical Models Ailerons Numerical integration Inverse Problems Sequential Quadratic Programming Angle of Attack integration algorithm

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Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2002年第11期55卷 1255-1284页

作者： Auricchio, F Petrini, L Univ Pavia Dipartimento Meccan Strutturale I-27100 Pavia Italy CNR Ist Matemat Applicata & Tecnol Informat I-27100 Pavia Italy

During mechanical loading-unloading cycles shape-memory alloys (SMA) are able to undergo large deformations without showing residual strains (pseudoelasticity) or recovering them through thermal cycles (shape memory effect). Motivated by stress-induced solid phase transformations, these unique behaviours induce the SMA exploitation in innovative and commercially valuable applications, stimulating, consequently, the interest in the development of constitutive models. Also if many models are now available in the literature, effective three-dimensional proposals are still few and limited in several aspects. In this paper, a three-dimensional thermomechanical model recently proposed by Souza et al. (European Journal of Mechanics-A/Solids, 1998;17:789-806.) is taken into consideration;such a model is of particular interest for its effectiveness and flexibility, but it also shows some limitations and missing links in the algorithmical counterparts. This work discusses some improvements to the original model as well as the development and the implementation of a robust integration algorithm to be adopted in a numerical scheme, such as a finite-element framework. Copyright (C) 2002 John Wiley Sons, Ltd.

关键词： shape memory alloys solid phase transformation 3D constitutive model numerical implementation return map integration algorithm

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Analytical modeling of sensor quantization in strapdown inertial navigation error equations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2002年第5期25卷 833-842页

作者： Savage, PG Strapdown Assoc Inc Maple Plain MN 55359 USA

Although generally not considered a major contributor to system inaccuracy, inertial sensor quantization error, if not properly modeled, can lead to erroneously large estimates of its impact on inertial navigation system performance. Analytical methods are described for modeling inertial sensor quantization in strapdown inertial system error parameter propagation and measurement equations. Error propagation equations are derived in classical differential error state dynamic and discrete difference format. It is shown how the attitude, velocity, and sensor error parameters in these equations must be modified to enable proper sensor quantization error modeling as white noise and to account for differences in attitude, velocity, and position update frequencies. The discrete difference error equation form is used to develop values for attitude/velocity measurement noise covariances and for spectral densities of white quantization noise terms in the differential error propagation equations. A general discussion is included of how quantization white noise spectral densities should be computed for the differential error propagation equations for compatibility with two-speed attitude, velocity, and position updating algorithms. Validity limits for white noise modeling approximations and methods for reducing quantization noise are discussed. Numerical examples are provided.

关键词： Inertial Sensor Strapdown Inertial Navigation System White Noise Spectral Density Aeronautical Engineering Aerospace Industry Accelerometer Earth Strapdown System integration algorithm

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Trajectory optimization for air-to-surface missiles with imaging radars

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2002年第5期25卷 876-887页

作者： Farooq, A Limebeer, DJN MBDA UK Ltd Seeker Div Borehamwood WD6 1RX Herts England Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2BT England

The use of trajectory optimization techniques is presented for the terminal guidance of an air-to-surface missile using a Doppler beam sharpening (DBS) radar seeker. The terminal guidance problem is characterized by a stealthy terrain-following phase that is followed by a climb and dive onto the target (a "bunt" trajectory). The imaging properties of DBS radars impose additional azimuth plane constraints on the trajectory that have to be incorporated into the optimization process. The various mission phases are interrelated, and the performance objectives come into conflict with the hardware constraints. The trajectory optimizer is used to generate offline open-loop controls that satisfy the various mission requirements. Numerical examples are used to illustrate the method and its efficacy.

关键词： Trajectory Optimization Air to Surface Missiles Synthetic Aperture Radar Target Acquisition Roll Control Numerical Optimization Sequential Quadratic Programming Closed Loop Autopilot integration algorithm

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New integrator for molecular dynamics simulations

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COMPUTER PHYSICS COMMUNICATIONS 2002年第1-2期147卷 733-736页

作者： Khakimov, ZM Uzbek Acad Sci Inst Nucl Phys Tashkent 702132 Uzbekistan

New third-order algorithms are proposed for integrating Newtonian equations of motion, which are more accurate and efficient than well-known algorithms, including high-order predictor-corrector ones. They enable one to increase noticeable typical time steps (similar to1 fs) in molecular dynamics simulations or to improve energy conservation by two orders of magnitude at high time steps. The algorithms are tested for the exactly solvable harmonic potential well model and for a silicon cluster using a tight-binding method for force calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： molecular dynamics integration algorithm energy conservation harmonic potential model tight-binding model

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New integrator for molecular dynamics simulations

New integrator for molecular dynamics simulations

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Europhysics Conference on Computational Physics (CCP 2001)

作者： Khakimov, ZM Uzbek Acad Sci Inst Nucl Phys Tashkent 702132 Uzbekistan

关键词： molecular dynamics integration algorithm energy conservation harmonic potential model tight-binding model

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Computations of axisymmetric plug-nozzle flowfields: Flow structures and thrust performance

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JOURNAL OF PROPULSION AND POWER 2002年第2期18卷 254-260页

作者： Ito, T Fujii, K Hayashi, AK Univ Tokyo Dept Aeronaut & Astronaut Bunkyo Ku Tokyo 1138654 Japan Inst Space & Astronaut Sci Kanagawa 2298510 Japan Aoyama Gakuin Univ Dept Engn Mech Tokyo 1578527 Japan

Plug-nozzle flowfields are analyzed by the numerical simulations. The method of characteristics is used to design the plug contour, and several types of plug nozzles are considered by truncating the length of the nozzle at different positions. Plug-nozzles' altitude-compensating features are confirmed by the computed results, and the base pressure turns out to play an important role to maintain the thrust performance of the nozzle for high-truncation configurations. The altitude clearly influences the base-pressure distributions under the assumption that the chamber pressure is constant during the ascent. The computed thrust difference between the contoured and the conical nozzle linearly increased as a function of the pressure ratio. The thrust performance of the contoured plug nozzle is estimated to be about 5-6% higher than the conical plug nozzle. Various conditions of external flows over the plug nozzle are also imposed, and the result shows that the external flow does not influence the pressure distribution on the nozzle surface for the pressure ratios higher than the designed point.

关键词： Contoured Plug Nozzle Mach Number Numerical Simulation Chamber Pressure Oblique Shock Wave Baldwin Lomax Turbulence Model Primitive Variable Navier Stokes Equations integration algorithm Propulsion System

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Family of constraint-preserving integrators for solving quaternion equations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2001年第1期24卷 72-78页

作者： Chiou, JC Jan, YR Wu, SD Natl Chiao Tung Univ Dept Elect & Control Engn Hsinchu 30010 Taiwan Precis Instrument Dev Ctr Div Res & Dev Hsinchu 30010 Taiwan

A family of numerical time integrators that exactly preserve the constraint of quaternion equations is developed, The constraint-preserving integrators based on the property of the skew-symmetric matrix and the proposed proven theorems are used to improve the accuracy of updating Euler parameters. The stability and accuracy analysis of the generalized constraint-preserving integrators is also discussed. Furthermore, we demonstrate that the proposed integrators are A-stable integrators that are proven to be useful in calculating angular orientations of kinematic and dynamic systems. A numerical example is used to demonstrate the superiority of the proposed integrators.

关键词： Quaternions Inertial Measurement Unit integration algorithm Numerical Simulation Taylor Series Runge Kutta Methods Kinematic Analysis Dynamic Analysis Computing

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On nonisothermal elastoplastic analysis of shell components employing realistic hardening responses

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2001年第28-29期38卷 5019-5039页

作者： Tonkovic, Z Soric, J Krätzig, WB Univ Zagreb Fac Mech Engn & Naval Architecture Zagreb 10000 Croatia Ruhr Univ Bochum Inst Stat & Dynam D-44780 Bochum Germany

In the present paper, efficient numerical algorithms for elastoplastic analysis of shell-like structural components will be proposed employing nonisothermal, realistic, highly nonlinear hardening responses. The closest point projection integration algorithm is presented using a Reissner-Mindlin type kinematic shell model, completely formulated in tenser notation. Further, a consistent elastoplastic tangent modulus is derived, which ensures high convergence rates in the global iteration approach. The integration algorithm has been implemented into a layered assumed strain isoparametric finite element, which also enables geometrical nonlinearities including finite rotations. The nonisothermal elastoplastic response of a circular cylindrical shell and a box column under axial compression is analysed. Under the assumption of an adiabatic process, the increase in temperature is computed during elastoplastic deformation. Robustness and numerical stability of the proposed algorithms are demonstrated. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： shell structures finite element analysis elastoplasticity nonisothermal hardening responses integration algorithm tensor formulation

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