The Resource Fractional Analysis : Methods of Motion Decomposition, by I.V. Novozhilov, (electronic resource)

Fractional Analysis : Methods of Motion Decomposition, by I.V. Novozhilov, (electronic resource)

Label
Fractional Analysis : Methods of Motion Decomposition
Title
Fractional Analysis
Title remainder
Methods of Motion Decomposition
Statement of responsibility
by I.V. Novozhilov
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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
http://library.link/vocab/creatorName
Novozhilov, I.V
Dewey number
515.2433
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
u5_LzgcUS5A
Image bit depth
0
Language note
English
LC call number
QA403.5-404.5
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Fourier analysis
  • Mathematics
  • Mechanical engineering
  • Mathematical physics
  • Integral Transforms
  • Fourier Analysis
  • Applications of Mathematics
  • Mechanical Engineering
  • Mathematical Methods in Physics
  • Real Functions
  • Integral Transforms, Operational Calculus
Label
Fractional Analysis : Methods of Motion Decomposition, by I.V. Novozhilov, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
I Dimensional analysis and small parameters -- 1 Dimensional analysis -- 2 Introduction of small parameters -- II Regularly perturbed systems. Expansions of solutions -- 3 The Poincaré theorem. The algorithm of expansion -- 4 Applications of the Poincaré theorem -- 5 Poincaré - Lyapunov method -- 5.1 Algorithm of the method -- 5.2 Examples. Nonisochronism of nonlinear system oscillations -- III Decomposition of motion in systems with fast phase -- 6 Method of averaging in systems with a single fast phase -- 7 Applications of the method of averaging -- 8 Method of harmonic linearization -- 9 Method of averaging in systems with several fast phases -- 10 Averaging in systems without explicit periodicities -- IV Decomposition of motion in systems with boundary layer -- 11 Tikhonov theorem -- 12 Application of the Tikhonov theorem -- 13 Asymptotic expansion of solutions for systems with a boundary layer -- V Decomposition of motion in systems with discontinuous characteristics -- 14 Definition of a solution in discontinuity points -- 15 Examples -- VI Correctness of limit models -- 16 Limit model of holonomic constraint (absolutely rigid body) -- 17 Limit model of kinematic constraints -- 18 Limit model of servoconstraint -- 19 Precession and nutation models in gyro theory -- 20 Mathematical model of a “man — artificial-kidney” system -- 21 Approximate models of an aircraft motion -- 22 Automobile motion decomposition -- References -- Author Index
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (X, 232 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461241300
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-4130-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000090717
  • (SSID)ssj0001296763
  • (PQKBManifestationID)11847469
  • (PQKBTitleCode)TC0001296763
  • (PQKBWorkID)11353090
  • (PQKB)10144793
  • (DE-He213)978-1-4612-4130-0
  • (MiAaPQ)EBC3075522
  • (EXLCZ)993400000000090717
Label
Fractional Analysis : Methods of Motion Decomposition, by I.V. Novozhilov, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
I Dimensional analysis and small parameters -- 1 Dimensional analysis -- 2 Introduction of small parameters -- II Regularly perturbed systems. Expansions of solutions -- 3 The Poincaré theorem. The algorithm of expansion -- 4 Applications of the Poincaré theorem -- 5 Poincaré - Lyapunov method -- 5.1 Algorithm of the method -- 5.2 Examples. Nonisochronism of nonlinear system oscillations -- III Decomposition of motion in systems with fast phase -- 6 Method of averaging in systems with a single fast phase -- 7 Applications of the method of averaging -- 8 Method of harmonic linearization -- 9 Method of averaging in systems with several fast phases -- 10 Averaging in systems without explicit periodicities -- IV Decomposition of motion in systems with boundary layer -- 11 Tikhonov theorem -- 12 Application of the Tikhonov theorem -- 13 Asymptotic expansion of solutions for systems with a boundary layer -- V Decomposition of motion in systems with discontinuous characteristics -- 14 Definition of a solution in discontinuity points -- 15 Examples -- VI Correctness of limit models -- 16 Limit model of holonomic constraint (absolutely rigid body) -- 17 Limit model of kinematic constraints -- 18 Limit model of servoconstraint -- 19 Precession and nutation models in gyro theory -- 20 Mathematical model of a “man — artificial-kidney” system -- 21 Approximate models of an aircraft motion -- 22 Automobile motion decomposition -- References -- Author Index
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (X, 232 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461241300
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-4130-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000090717
  • (SSID)ssj0001296763
  • (PQKBManifestationID)11847469
  • (PQKBTitleCode)TC0001296763
  • (PQKBWorkID)11353090
  • (PQKB)10144793
  • (DE-He213)978-1-4612-4130-0
  • (MiAaPQ)EBC3075522
  • (EXLCZ)993400000000090717

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