fractional analysis methods of motion decomposition

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Fractional Analysis

Author : I.V. Novozhilov
ISBN : 081763889X
Genre : Mathematics
File Size : 48. 45 MB
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This book considers methods of approximate analysis of mechanical, elec tromechanical, and other systems described by ordinary differential equa tions. Modern mathematical modeling of sophisticated mechanical systems consists of several stages: first, construction of a mechanical model, and then writing appropriate equations and their analytical or numerical ex amination. Usually, this procedure is repeated several times. Even if an initial model correctly reflects the main properties of a phenomenon, it de scribes, as a rule, many unnecessary details that make equations of motion too complicated. As experience and experimental data are accumulated, the researcher considers simpler models and simplifies the equations. Thus some terms are discarded, the order of the equations is lowered, and so on. This process requires time, experimentation, and the researcher's intu ition. A good example of such a semi-experimental way of simplifying is a gyroscopic precession equation. Formal mathematical proofs of its admis sibility appeared some several decades after its successful introduction in engineering calculations. Applied mathematics now has at its disposal many methods of approxi mate analysis of differential equations. Application of these methods could shorten and formalize the procedure of simplifying the equations and, thus, of constructing approximate motion models. Wide application of the methods into practice is hindered by the fol lowing. 1. Descriptions of various approximate methods are scattered over the mathematical literature. The researcher, as a rule, does not know what method is most suitable for a specific case. 2.

Asymptotic Methods For Ordinary Differential Equations

Author : R.P. Kuzmina
ISBN : 0792364007
Genre : Mathematics
File Size : 88. 55 MB
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This book considers the Cauchy problem for a system of ordinary differential equations with a small parameter, filling in areas that have not been extensively covered in the existing literature. The well-known types of equations, such as the regularly perturbed Cauchy problem and the Tikhonov problem, are dealt with, but new ones are also treated, such as the quasiregular Cauchy problem, and the Cauchy problem with double singularity. For each type of problem, series are constructed which generalise the well-known series of Poincaré and Vasilyeva-Imanaliyev. It is shown that these series are asymptotic expansions of the solution, or converge to the solution on a segment, semiaxis or asymptotically large time intervals. Theorems are proved providing numerical estimates for the remainder term of the asymptotics, the time interval of the solution existence, and the small parameter values. Audience: This volume will be of interest to researchers and graduate students specialising in ordinary differential equations.

Zeitschrift F R Analysis Und Ihre Anwendungen

Author :
ISBN : UOM:39015049324539
Genre : Mathematical analysis
File Size : 79. 44 MB
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Revue D Analyse Num Rique Et De Th Orie De L Approximation

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ISBN : UOM:39015053349232
Genre : Approximation theory
File Size : 79. 31 MB
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Haar Wavelets

Author : Ülo Lepik
ISBN : 9783319042954
Genre : Technology & Engineering
File Size : 50. 56 MB
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This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.

Applied Mechanics Reviews

Author :
ISBN : UIUC:30112046051832
Genre : Mechanics, Applied
File Size : 22. 35 MB
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Books In Print

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ISBN : UOM:39015054023182
Genre : American literature
File Size : 41. 61 MB
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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Mathematical Reviews

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ISBN : UOM:39015067268402
Genre : Mathematics
File Size : 48. 8 MB
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Applied Mathematics

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ISBN : UOM:39015072621207
Genre : Mathematics
File Size : 59. 36 MB
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Ieee Sensors Journal

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ISBN : OSU:32435072395460
Genre : Detectors
File Size : 28. 24 MB
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