Fractional Analysis: methods of motion decomposition
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
1997
|
| Schlagworte: | |
| Beschreibung: | This book considers methods of approximate analysis of mechanical, electromechanical, and other systems described by ordinary differential equations. 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 examination. Usually, this procedure is repeated several times. Even if an initial model correctly reflects the main properties of a phenomenon, it describes, 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 intuition. A good example of such a semi-experimental way of simplifying is a gyroscopic precession equation. Formal mathematical proofs of its admissibility appeared some several decades after its successful introduction in engineering calculations. Applied mathematics now has at its disposal many methods of approximate 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 following. 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 |
| Beschreibung: | xx, 231 Seiten Illustrationen, Diagramme |
| ISBN: | 9781461241300 9781461286677 |
Internformat
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| 500 | |a This book considers methods of approximate analysis of mechanical, electromechanical, and other systems described by ordinary differential equations. 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 examination. Usually, this procedure is repeated several times. Even if an initial model correctly reflects the main properties of a phenomenon, it describes, 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 intuition. A good example of such a semi-experimental way of simplifying is a gyroscopic precession equation. Formal mathematical proofs of its admissibility appeared some several decades after its successful introduction in engineering calculations. Applied mathematics now has at its disposal many methods of approximate 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 following. 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 | ||
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Datensatz im Suchindex
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| author | Novožilov, Igor Vasilevič 1931- |
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| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV048662162 |
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| dewey-full | 515.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV048662162 |
| illustrated | Illustrated |
| index_date | 2024-07-03T21:21:20Z |
| indexdate | 2024-07-10T09:45:14Z |
| institution | BVB |
| isbn | 9781461241300 9781461286677 |
| language | English |
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| physical | xx, 231 Seiten Illustrationen, Diagramme |
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| spelling | Novožilov, Igor Vasilevič 1931- (DE-588)1089238177 aut Fractional Analysis methods of motion decomposition Igor V. Novozhilov Boston ; Basel ; Berlin Birkhäuser 1997 xx, 231 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier This book considers methods of approximate analysis of mechanical, electromechanical, and other systems described by ordinary differential equations. 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 examination. Usually, this procedure is repeated several times. Even if an initial model correctly reflects the main properties of a phenomenon, it describes, 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 intuition. A good example of such a semi-experimental way of simplifying is a gyroscopic precession equation. Formal mathematical proofs of its admissibility appeared some several decades after its successful introduction in engineering calculations. Applied mathematics now has at its disposal many methods of approximate 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 following. 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 Mathematics Fourier analysis Functions of complex variables Integral Transforms Mathematical physics Fourier Analysis Mathematical Methods in Physics Real Functions Integral Transforms, Operational Calculus Functions of a Complex Variable Mathematik Mathematische Physik Psychische Vorbereitung (DE-588)4176194-7 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Langstreckenlauf (DE-588)4034542-7 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Approximation (DE-588)4002498-2 s 1\p DE-604 Langstreckenlauf (DE-588)4034542-7 s Psychische Vorbereitung (DE-588)4176194-7 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-8667-7 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Novožilov, Igor Vasilevič 1931- Fractional Analysis methods of motion decomposition Mathematics Fourier analysis Functions of complex variables Integral Transforms Mathematical physics Fourier Analysis Mathematical Methods in Physics Real Functions Integral Transforms, Operational Calculus Functions of a Complex Variable Mathematik Mathematische Physik Psychische Vorbereitung (DE-588)4176194-7 gnd Approximation (DE-588)4002498-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Langstreckenlauf (DE-588)4034542-7 gnd |
| subject_GND | (DE-588)4176194-7 (DE-588)4002498-2 (DE-588)4020929-5 (DE-588)4034542-7 |
| title | Fractional Analysis methods of motion decomposition |
| title_auth | Fractional Analysis methods of motion decomposition |
| title_exact_search | Fractional Analysis methods of motion decomposition |
| title_exact_search_txtP | Fractional Analysis methods of motion decomposition |
| title_full | Fractional Analysis methods of motion decomposition Igor V. Novozhilov |
| title_fullStr | Fractional Analysis methods of motion decomposition Igor V. Novozhilov |
| title_full_unstemmed | Fractional Analysis methods of motion decomposition Igor V. Novozhilov |
| title_short | Fractional Analysis |
| title_sort | fractional analysis methods of motion decomposition |
| title_sub | methods of motion decomposition |
| topic | Mathematics Fourier analysis Functions of complex variables Integral Transforms Mathematical physics Fourier Analysis Mathematical Methods in Physics Real Functions Integral Transforms, Operational Calculus Functions of a Complex Variable Mathematik Mathematische Physik Psychische Vorbereitung (DE-588)4176194-7 gnd Approximation (DE-588)4002498-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Langstreckenlauf (DE-588)4034542-7 gnd |
| topic_facet | Mathematics Fourier analysis Functions of complex variables Integral Transforms Mathematical physics Fourier Analysis Mathematical Methods in Physics Real Functions Integral Transforms, Operational Calculus Functions of a Complex Variable Mathematik Mathematische Physik Psychische Vorbereitung Approximation Gewöhnliche Differentialgleichung Langstreckenlauf |
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