THIS Engineering Note follows a previous paper in which Avanzini [1] presented a transverse-eccentricity-vector-based algorithm to solve the classical Lambert problem: that is, the determination of a transfer orbit ha...
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THIS Engineering Note follows a previous paper in which Avanzini [1] presented a transverse-eccentricity-vector-based algorithm to solve the classical Lambert problem: that is, the determination of a transfer orbit having a specified flight time and connecting two position vectors [2]. In Avanzini's [1] paper, the eccentricity vector of the transfer orbit can be decomposed into a constant component parallel to the chord connecting the two points and a variable transverse component in the direction perpendicular to it on the orbit plane. Given the two fixed position vectors, the transfer time can be expressed as a function of the transverse eccentricity e(T). Compared with the elegant Battin's method, the derivation of this simple Lambert algorithm seems to be considerably less demanding from the mathematical standpoint and physically more intuitive [1]. However, with the only consideration of direct-transfer arcs, neither the explicit expression of the derivative of the transfer time with respect to the transverse eccentricity nor the multiple-revolution solutions based on the novel method were given in [1].
This paper deals with the prediction of the overall behavior of a class of two-phase elasto-viscoplastic composites, based on mean-field homogenization. For this, important improvements are made to the recently-propos...
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This paper deals with the prediction of the overall behavior of a class of two-phase elasto-viscoplastic composites, based on mean-field homogenization. For this, important improvements are made to the recently-proposed affine formulation. The latter theory linearizes the rate-dependent inelastic constitutive equations of each phase's material and transforms them into fictitious linear thermo-elastic relations in the Laplace-Carson domain. The main contributions of the present work are threefold. Firstly, complete mathematical developments including a full treatment of internal variables are carried out, enabling the modeling of the response under unloading and cyclic histories. Secondly, robust and accurate computational algorithms are proposed. Thirdly, an extensive validation of the predictions against reference unit cell finite element results is conducted for a variety of materials and loadings. A good agreement between predictions and reference results is observed. (c) 2005 Elsevier Ltd. All rights reserved.
Structure-preserving numerical techniques for computation of stable deflating subspaces, with applications in control systems design, are presented. The techniques use extended skew-Hamiltonian/Hamiltonian matrix penc...
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Structure-preserving numerical techniques for computation of stable deflating subspaces, with applications in control systems design, are presented. The techniques use extended skew-Hamiltonian/Hamiltonian matrix pencils, and specialized algorithms to exploit their structure: the symplectic URV decomposition, periodic QZ algorithm, solution of periodic Sylvester-like equations, etc. The structure-preserving approach has the potential to avoid the numerical difficulties which are encountered for a traditional, non-structured solution, returned by the currently available software tools.
In this paper we discuss the one dimensional heat equation and the wave equation subject to nonlocal conditions. We use the method of Laplace transforms. Finally, we obtain the solution by using a numerical technique ...
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In this paper we discuss the one dimensional heat equation and the wave equation subject to nonlocal conditions. We use the method of Laplace transforms. Finally, we obtain the solution by using a numerical technique for inverting the Laplace transforms.
The control of complex forming processes (e.g. glass forming processes) is a challenging topic due to the mostly strongly nonlinear behavior and the spatial distributed nature of the process. In this paper a new appro...
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The control of complex forming processes (e.g. glass forming processes) is a challenging topic due to the mostly strongly nonlinear behavior and the spatial distributed nature of the process. In this paper a new approach for the real-time control of a spatial distributed temperature profile of an industrial glass forming process is presented. As the temperature in the forming zone cannot be measured directly, it is estimated by the numerical solution of the partial differential equation for heat transfer by a finite element scheme. As the dimension of the state space model, which is yield by the FE algorithm, is too large for real-time optimization, a model reduction concept has been developed. The numerical solution of the optimization problem is performed by the solver HQP (Huge Quadratic Programming). Results of the NMPC concept are compared with conventional PI control results. It is shown that NMPC stabilizes the temperature of the forming zone much better than PI control. The proposed NMPC scheme is robust against model mismatch of the disturbance model. Furthermore, the allowed parameter settings for a real-time application (i.e. control horizon, sampling period) have been determined. The approach can easily be adapted to other forming processes where the temperature profile shall be controlled.
Phase change problems are of practical importance and can be found in a wide range of engineering applications. In the present paper, two proposed numerical algorithms are developed;the first one is general for phase ...
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Phase change problems are of practical importance and can be found in a wide range of engineering applications. In the present paper, two proposed numerical algorithms are developed;the first one is general for phase change problems, while the second one is for ablation problems. The boundary elements method is used as a mathematical tool in conjunction with the proposed algorithms. Two test examples were solved and the results agree with the physics of the problems. (C) 2009 Elsevier Ltd. All rights reserved.
A numerical algorithm to obtain the consistent conditions satisfied by singular arcs for singular linear-quadratic optimal control problems is presented. The algorithm is based on the Presymplectic Constraint Algorith...
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A numerical algorithm to obtain the consistent conditions satisfied by singular arcs for singular linear-quadratic optimal control problems is presented. The algorithm is based on the Presymplectic Constraint Algorithm (PCA) by Gotay-Nester (Gotay et al., J Math Phys 19:2388-2399, 1978;Volckaert and Aeyels 1999) that allows to solve presymplectic Hamiltonian systems and that provides a geometrical framework to the Dirac-Bergmann theory of constraints for singular Lagrangian systems (Dirac, Can J Math 2:129-148, 1950). The numerical implementation of the algorithm is based on the singular value decomposition that, on each step, allows to construct a semi-explicit system. Several examples and experiments are discussed, among them a family of arbitrary large singular LQ systems with index 2 and a family of examples of arbitrary large index, all of them exhibiting stable behaviour.
The QR factorization is one of the most important operations in dense linear algebra, offering a numerically stable method for solving linear systems of equations including overdetermined and underdetermined systems. ...
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The QR factorization is one of the most important operations in dense linear algebra, offering a numerically stable method for solving linear systems of equations including overdetermined and underdetermined systems. Modern implementations of the QR factorization, such as the one in the LAPACK library, suffer from performance limitations due to the use of matrix-vector type operations in the phase of panel factorization. These limitations can be remedied by using the idea of updating of QR factorization, rendering an algorithm, which is much more scalable and much more suitable for implementation on a multi-core processor. It is demonstrated how the potential of the cell broadband engine can be utilized to the fullest by employing the new algorithmic approach and successfully exploiting the capabilities of the chip in terms of single instruction multiple data parallelism, instruction level parallelism and thread-level parallelism.
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