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Dynamics of rheonomic systems
BOOK
REVIEWS
539
pioneering work, conducted at the Institute of Sound and Vibration Research, Southampton University, U.K., has been such that reliable and comparable work has often not been conducted elsewhere. Where data has been available from other laboratories it has been presented. Material has been presented with an underlying and considered philosophy. This is not a collection of unrelated studies presented in an uncritical way. The price for this, however, is long philosophical discussion in places. This is fine for the researcher but may be excessive for the practitioner. The book is long and could have been shortened. With this book the investigation of human response to vibration has changed. I\lo longer does one have to search through separate and diverse publications. The essential human vibration is now in one volume which is undoubtedly the classic work in this area. K. C. PARSOhS DYNAMICS
Mathematical
SYSTEMS 1990, by V. Vujicic. Beograd (Belgrade), Price unspecified; pp 96+ ii. ISBN 86-80593-04-4.
OF RHEONOMIC
Institut.
Yugoslavia:
This is a concise and helpful monograph on the analytical dynamics of discrete mechanical systems under general ideal and explicitly time-dependent (or non-stationary, or rheononic 1, geometrical (or finite, or holonomic) and/or linear velocity (ultimately holonomic or not) constraints. It should be of interest to applied mathematicians, physicists and all theoretically or qualitatively minded engineers (such as mechanicians, mechanical/aero/electrical), from the postgraduate level and above. The sole prerequisite here is a knowledge of ordinary advanced calculus and intermediate-to-advanced classical dynamics, e.g., on the level of the well-known textbooks of Synge and Griffith, or Fowles. A knowledge of differential geometry/tensor calculus would be quite helpful but, strictly speaking, it is not necessary. The presentation is traditionalist, clear and straightforward, i.e., no epsilonics and/or faddish formalisms, and shows the author’s long and creative involvement with the sub.ject. Specifically, the book is divided into two parts; (i) Survey of Elementary Modifications, and (ii) Principles of Mechanics. The first part contains the following four sections, ( 1) Limiting of the Motion of a Point, (2) Motion of a Material Particle over Rheonomic Surface, (3) Rheonomic Systems, and (4) Non-holonomic Rheonomic Constraints; while the second part contains the following six sections, (5) Equivalence and Invariance of Principles, (6) D’Alembert’s Principle, (7) Principle of Possible Displacements, (8) Invariance of Principle of Lost Forces, (9) Principle of Least Constraint’( of Gauss/Gibbs), (10) Principle of Least Action (further subdivided into Principle of Stationary Action, Law of Energy, and Coupled Differential Equations). The discussion ends with an Epilogue, and a list of 20 references (half of which are the author’s earlier papers and another monograph on the subject). If pressed to cite drawbacks, or omissions, of the book this reviewer would mention: (i) the complete absence of Jigures; (ii) the complete absence of any discussion of quasi-co-ordinates and associated equatioris of motion for rheonomic systems; and (iii) the absence of some fundamental relevant references, e.g., A. I. Lur’e, Anafyfical Mechanics (in Russian, or French), V. V. Dobronravov, Principles of Analytical Mechanics (in Russian), V. V. Dobronravov, Principles of NonhoZonomic System Mechanics (in Russian) and J. L. Synge, Censorial Methods in Dynamics. Nevertheless, these oversights are definitely non-fatal, and in view of the virtual non-existence and/or non-availability of English language references in print on I:he subject, this booklet is most welcome and certainly fills the needs of students, teachers and researchers in advanced dynamics. It would complement ideally larger works such as the well-known monograph by Lanczos on the variational principles of mechanics. It
540
ROOK
REVIEWS
is therefore very warmly recommended by this reviewer. Prospective readers, however, may have to contact the author himself, or his organization (Mathematical Institute, Belgrade, Yugoslavia), to obtain their copies. J. G. PAPASTAVRIDIS ELASTIC
WAVE
PROPAGATION
Amsterdam: North-Holland ISBN O-444-87272-8.
1989, Elsevier.
editors M. F. McCarthy and M. A. Hayes. pp. 638 + xviii. Price US$ 167.75/Dfl. 315.00.
This book is the Proceedings of the Second IUTAM-IUPAP Symposium on Elastic Wave Propagation, which was held in Galway, Republic of Ireland, on 20-25 March 1988; the first such IUTAM symposium was at Northwestern University in 1977. Seven Sessional lectures were delivered and over 80 other papers were contributed covering a very wide range of elastic wave phenomena from surface wave existence theory to wave propagation through anisotropic microcracked rocks. These Proceedings do not distinguish between the Sessional lectures and the other contributions and so, for the record, the Sessional Lectures were as follows: (i) Peter Chadwick (U.K.)-“Recent Developments in the Theory of Elastic Surface and Interfacial Waves”; (ii) James Corones (U.S.A.)“Transient Direct and Inverse Scattering”; (iii ) Eugene Dieulesaint (France )-“Probing of Acoustic Wave Surface Displacements”; (iv) Guillermo Gaunard (U.S.A.)--“Resonante Acoustic Scattering from Underwater Bodies”; (v) John McCoy (U.S.A.)--“Propagation Modeling Based on Wave Factorization and Path Integration”; (vi) Andrew Norris (U.S.A.)-“Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids”; (vii) H. F. Tiersten (U.S.A.)-“Electroelastic Vibrations”. The proceedings classify all the contributions into seven subject areas: (A) Elastic Surface Waves; (B) Non-linear Elastic Waves; (C) Wave Propagation in Layered and Bounded Media; (D) Fluid/Solid Wave Interaction; (E) Scattering of Elastic Waves; (F) General Theory of Elastic Wave Propagation; (G) Magneto-Thermo-ElectromagnetoElastic Wave Propagation. This classification is carried out fairly roughly however, and the browser is quite likely to find papers which interest him in an unexpected section. Also, in the introductory list of contents, one page of contributions carries no page numbers and, in the author index, many of the page numbers are slightly incorrect. However, these small annoyances are more than offset by the high quality of the contributed papers. This is a volume which almost any worker in elastic wave propagation can browse over and benefit from. A few contributions which caught the reviewer’s eye were: two papers (Ma1 and Xu and Olsson, Datta and Bostrom) in which a thin interfacial layer was modelled approximately by a special boundary condition and thin shell theory, respectively; Martin’s reduction of scattering by an elastic inclusion to a single integral equation; optimal geometrical and physical bounds for Rayleigh scattering (Dassios ); the amplification of ground motion when a Rayleigh wave encounters an alluvial valley (Bostrom, Datta and Olsson); the still unsolved problem of buckle propagation in underwater pipelines (Suginoto); and Cowin’s elegant characterization of elastic symmetry using only mirror symmetries. The above list clearly reflects the reviewer’s own interest in linear elastic wave propagation and scattering theory and could have been much longer. Nevertheless, it illustrates the variety of current topics which appear in this interesting volume. R.D. GREGORY
REVIEWS
539
pioneering work, conducted at the Institute of Sound and Vibration Research, Southampton University, U.K., has been such that reliable and comparable work has often not been conducted elsewhere. Where data has been available from other laboratories it has been presented. Material has been presented with an underlying and considered philosophy. This is not a collection of unrelated studies presented in an uncritical way. The price for this, however, is long philosophical discussion in places. This is fine for the researcher but may be excessive for the practitioner. The book is long and could have been shortened. With this book the investigation of human response to vibration has changed. I\lo longer does one have to search through separate and diverse publications. The essential human vibration is now in one volume which is undoubtedly the classic work in this area. K. C. PARSOhS DYNAMICS
Mathematical
SYSTEMS 1990, by V. Vujicic. Beograd (Belgrade), Price unspecified; pp 96+ ii. ISBN 86-80593-04-4.
OF RHEONOMIC
Institut.
Yugoslavia:
This is a concise and helpful monograph on the analytical dynamics of discrete mechanical systems under general ideal and explicitly time-dependent (or non-stationary, or rheononic 1, geometrical (or finite, or holonomic) and/or linear velocity (ultimately holonomic or not) constraints. It should be of interest to applied mathematicians, physicists and all theoretically or qualitatively minded engineers (such as mechanicians, mechanical/aero/electrical), from the postgraduate level and above. The sole prerequisite here is a knowledge of ordinary advanced calculus and intermediate-to-advanced classical dynamics, e.g., on the level of the well-known textbooks of Synge and Griffith, or Fowles. A knowledge of differential geometry/tensor calculus would be quite helpful but, strictly speaking, it is not necessary. The presentation is traditionalist, clear and straightforward, i.e., no epsilonics and/or faddish formalisms, and shows the author’s long and creative involvement with the sub.ject. Specifically, the book is divided into two parts; (i) Survey of Elementary Modifications, and (ii) Principles of Mechanics. The first part contains the following four sections, ( 1) Limiting of the Motion of a Point, (2) Motion of a Material Particle over Rheonomic Surface, (3) Rheonomic Systems, and (4) Non-holonomic Rheonomic Constraints; while the second part contains the following six sections, (5) Equivalence and Invariance of Principles, (6) D’Alembert’s Principle, (7) Principle of Possible Displacements, (8) Invariance of Principle of Lost Forces, (9) Principle of Least Constraint’( of Gauss/Gibbs), (10) Principle of Least Action (further subdivided into Principle of Stationary Action, Law of Energy, and Coupled Differential Equations). The discussion ends with an Epilogue, and a list of 20 references (half of which are the author’s earlier papers and another monograph on the subject). If pressed to cite drawbacks, or omissions, of the book this reviewer would mention: (i) the complete absence of Jigures; (ii) the complete absence of any discussion of quasi-co-ordinates and associated equatioris of motion for rheonomic systems; and (iii) the absence of some fundamental relevant references, e.g., A. I. Lur’e, Anafyfical Mechanics (in Russian, or French), V. V. Dobronravov, Principles of Analytical Mechanics (in Russian), V. V. Dobronravov, Principles of NonhoZonomic System Mechanics (in Russian) and J. L. Synge, Censorial Methods in Dynamics. Nevertheless, these oversights are definitely non-fatal, and in view of the virtual non-existence and/or non-availability of English language references in print on I:he subject, this booklet is most welcome and certainly fills the needs of students, teachers and researchers in advanced dynamics. It would complement ideally larger works such as the well-known monograph by Lanczos on the variational principles of mechanics. It
540
ROOK
REVIEWS
is therefore very warmly recommended by this reviewer. Prospective readers, however, may have to contact the author himself, or his organization (Mathematical Institute, Belgrade, Yugoslavia), to obtain their copies. J. G. PAPASTAVRIDIS ELASTIC
WAVE
PROPAGATION
Amsterdam: North-Holland ISBN O-444-87272-8.
1989, Elsevier.
editors M. F. McCarthy and M. A. Hayes. pp. 638 + xviii. Price US$ 167.75/Dfl. 315.00.
This book is the Proceedings of the Second IUTAM-IUPAP Symposium on Elastic Wave Propagation, which was held in Galway, Republic of Ireland, on 20-25 March 1988; the first such IUTAM symposium was at Northwestern University in 1977. Seven Sessional lectures were delivered and over 80 other papers were contributed covering a very wide range of elastic wave phenomena from surface wave existence theory to wave propagation through anisotropic microcracked rocks. These Proceedings do not distinguish between the Sessional lectures and the other contributions and so, for the record, the Sessional Lectures were as follows: (i) Peter Chadwick (U.K.)-“Recent Developments in the Theory of Elastic Surface and Interfacial Waves”; (ii) James Corones (U.S.A.)“Transient Direct and Inverse Scattering”; (iii ) Eugene Dieulesaint (France )-“Probing of Acoustic Wave Surface Displacements”; (iv) Guillermo Gaunard (U.S.A.)--“Resonante Acoustic Scattering from Underwater Bodies”; (v) John McCoy (U.S.A.)--“Propagation Modeling Based on Wave Factorization and Path Integration”; (vi) Andrew Norris (U.S.A.)-“Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids”; (vii) H. F. Tiersten (U.S.A.)-“Electroelastic Vibrations”. The proceedings classify all the contributions into seven subject areas: (A) Elastic Surface Waves; (B) Non-linear Elastic Waves; (C) Wave Propagation in Layered and Bounded Media; (D) Fluid/Solid Wave Interaction; (E) Scattering of Elastic Waves; (F) General Theory of Elastic Wave Propagation; (G) Magneto-Thermo-ElectromagnetoElastic Wave Propagation. This classification is carried out fairly roughly however, and the browser is quite likely to find papers which interest him in an unexpected section. Also, in the introductory list of contents, one page of contributions carries no page numbers and, in the author index, many of the page numbers are slightly incorrect. However, these small annoyances are more than offset by the high quality of the contributed papers. This is a volume which almost any worker in elastic wave propagation can browse over and benefit from. A few contributions which caught the reviewer’s eye were: two papers (Ma1 and Xu and Olsson, Datta and Bostrom) in which a thin interfacial layer was modelled approximately by a special boundary condition and thin shell theory, respectively; Martin’s reduction of scattering by an elastic inclusion to a single integral equation; optimal geometrical and physical bounds for Rayleigh scattering (Dassios ); the amplification of ground motion when a Rayleigh wave encounters an alluvial valley (Bostrom, Datta and Olsson); the still unsolved problem of buckle propagation in underwater pipelines (Suginoto); and Cowin’s elegant characterization of elastic symmetry using only mirror symmetries. The above list clearly reflects the reviewer’s own interest in linear elastic wave propagation and scattering theory and could have been much longer. Nevertheless, it illustrates the variety of current topics which appear in this interesting volume. R.D. GREGORY