Classical mechanics Books

Book SynopsisThin shells are three-dimensional structures with a dimension (the thickness) small with respect to the two others.Such thin structures are widely used in automobileandaviation industries,or in civil engineering, because they provide animportantsti?ness, due to theircurvature,with a small weight. Fig. 0.1. Airbus A380 Fig. 0.2. Hemispherical roof (Marseille, France) One ofthechallenges is often to reduce the weight (andconsequently the thickness)oftheshells, preservingtheirsti?ness.So that it is essential to have 1 accuratemodelsforthinandevenverythinshells ,andtobeabletocomputethe displacements resultingfromagivenloading.In particular, singularities leading to fractures in some cases must be absolutely predicted a priori and ofcourse avoided (see Fig.0.3 forexample). Since the pioneeringmodels of Novozhilov-Donnell [81] and Koiter [65][66], numerous works havebeen devoted to establish linear and non linear elastic shell model usingdirect orsurfacic approaches [18][25][100]. More recently, the asymptoticmethods [87] havebeen used, to try tojustify rigorously, fromthe three-dimensional equations, the shell models obtained by direct approaches - lying onapriori assumption, andto construct new models [54][55]. This way, 1 Very thin shells are present in certain domains of industry, as plastic ?lms for pa- aging or for electronics, streched sails, or even very thin metal sheets obtained by drawing. E. Sanchez-Palencia et al.: Singular Problems in Shell Theory, LNACM 54, pp. 1-11.Trade ReviewFrom the reviews:“The book under review is devoted to a mathematically rigorous study of singularities in linear elastic shell theory which appear for very small thickness. … This well-written book is a reader-friendly and good organized research work in the field of mathematical theory of shells. It can be recommended to highly-qualified experts in this field.” (Igor Andrianov, Zentralblatt MATH, Vol. 1208, 2011)Table of ContentsGeometric Formalism of Shell Theory.- Singularities and Boundary Layers in Thin Elastic Shell Theory.- Anisotropic Error Estimates in the Layers.- Numerical Simulation with Anisotropic Adaptive Mesh.- Singularities of Parabolic Inhibited Shells.- Singularities of Hyperbolic Inhibited Shells.- Singularities of Elliptic Well-Inhibited Shells.- Generalities on Boundary Conditions for Equations and Systems: Introduction to Sensitive Problems.- Numerical Simulations for Sensitive Shells.- Examples of Non-inhibited Shell Problems (Non-geometrically Rigid Problems).

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Book SynopsisThis book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.Table of ContentsErgodicity – A Basic Concept.- Large Deviations in Statistical Mechanics: Rigorous and Non-Rigorous.- Large Deviation Techniques for Long-Range Interactions.- Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium Phenomena and Back.- Stochastic Fluctuations in Deterministic Systems.- Large Deviation and Disordered Systems.- Large Deviations in Turbulence.- Ergodicity Breaking Challenges Monte Carlo Methods.- Anomalous Diffusion: Deterministic and Stochastic Perspectives.- The Use of Fluctuation Relations for the Analysis of Free-Energy Landscapes.

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Book SynopsisIn structure mechanics analysis, finite element methods are now well estab­ lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap­ proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require­ ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.Table of ContentsNotations.- 1. Elliptic Equations of Order 2: Some Standard Finite Element Methods.- 1.1. A 1-Dimensional Model Problem: The Basic Notions.- 1.2. A 2-Dimensional Problem.- 1.3. The Finite Element Equations.- 1.4. Standard Examples of Finite Element Methods.- 1.4.1. Example 1: The P1-Triangle (Courant’s Triangle).- 1.4.2. Example 2: The P2-Triangle.- 1.4.3. Example 3: The Q1-Quadrangle.- 1.4.4. Example 4: The Q2-Quadrangle.- 1.4.5. A Variational Crime: The P1 Nonconforming Element.- 1.5. Mixed Formulation and Mixed Finite Element Methods for Elliptic Equations.- 1.5.1. The One Dimensional Problem.- 1.5.2. A Two Dimensional Problem.- 2. Upwind Finite Element Schemes.- 2.1. Upwind Finite Differences.- 2.2. Modified Weighted Residual (MWR).- 2.3. Reduced Integration of the Advection Term.- 2.4. Computation of Directional Derivatives at the Nodes.- 2.5. Discontinuous Finite Elements and Mixed Interpolation.- 2.6. The Method of Characteristics in Finite Elements.- 2.7. Peturbation of the Advective Term: Bredif (1980).- 2.8. Some Numerical Tests and Further Comments.- 2.8.1. One Dimensional Stationary Advection Equation (56).- 2.8.2. Two Dimensional Stationary Advection Equation.- 2.8.3. Time Dependent Advection.- 3. Numerical Solution of Stokes Equations.- 3.1. Introduction.- 3.2. Velocity—Pressure Formulations: Discontinuous Approximations of the Pressure.- 3.2.1. uh: P1 Nonconforming Triangle (§1-4-5); ph: Piecewise Constant.- 3.2.2. uh: P2 Triangle ph: P0 (Piecewise Constant).- 3.2.3. uh: “P2+bubble” Triangle (or Modified P2); ph: Discontinuous P1.- 3.2.4. uh: Q2 Quadrangle; ph: Q1 Discontinuous.- 3.2.5. Numerical Solution by Penalty Methods.- 3.2.6. Numerical Results and Further Comments.- 3.3. Velocity—Pressure Formulations: Continuous Approximation of the Pressure and Velocity.- 3.3.1. Introduction.- 3.3.2. Examples and Error Estimates.- 3.3.3. Decomposition of the Stokes Problem.- 3.4. Vorticity—Pressure—Velocity Formulations: Discontinuous Approximations of Pressure and Velocity.- 3.5. Vorticity Stream-Function Formulation: Decompositions of the Biharmonic Problem.- 4. Navier-Stokes Equations: Accuracy Assessments and Numerical Results.- 4.1. Remarks on the Formulation.- 4.2. A review of the Different Methods.- 4.2.1 Velocity—Pressure Formulations: Discontinuous Approximations of the Pressure.- 4.2.2. Velocity—Pressure Formulations: Continuous Approximations of the Pressure.- 4.2.3. Vorticity—Pressure—Velocity Formulations: Discontinuous Approximations of Pressure and Velocity.- 4.2.4. Vorticity Stream-Function Formulation.- 4.3. Some Numerical Tests.- 4.3.1. The Square Wall Driven Cavity Flow.- 4.3.2. An Engineering Problem: Unsteady 2-D Flow Around and In an Air-Intake.- 5. Computational Problems and Bookkeeping.- 5.1. Mesh Generation.- 5.2. Solution of the Nonlinear Problems.- 5.2.1. Successive Approximations (or Linearization) with Under Relaxation.- 5.2.2. Newton-Raphson Algorithm.- 5.2.3. Conjugate Gradient Method (with Scaling) for Nonlinear Problems.- 5.2.4. A Splitting Technique for the Transient Problem.- 5.3. Iterative and Direct Solvers of Linear Equations.- 5.3.1. Successive Over Relaxation.- 5.3.2. Cholesky Factorizations.- 5.3.3. Out of Core Factorizations.- 5.3.4. Preconditioned Conjugate Gradient.- Appendix 2. Numerical Illustration.- Three Dimensional Case.- References.

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Book SynopsisOne studying the motion of fluids relative to particulate systems is soon impressed by the dichotomy which exists between books covering theoretical and practical aspects. Classical hydrodynamics is largely concerned with perfect fluids which unfortunately exert no forces on the particles past which they move. Practical approaches to subjects like fluidization, sedimentation, and flow through porous media abound in much useful but uncorrelated empirical information. The present book represents an attempt to bridge this gap by providing at least the beginnings of a rational approach to fluid­ particle dynamics, based on first principles. From the pedagogic viewpoint it seems worthwhile to show that the Navier-Stokes equations, which form the basis of all systematic texts, can be employed for useful practical applications beyond the elementary problems of laminar flow in pipes and Stokes law for the motion of a single particle. Although a suspension may often be viewed as a continuum for practical purposes, it really consists of a discrete collection of particles immersed in an essentially continuous fluid. Consideration of the actual detailed boundary­ value problems posed by this viewpoint may serve to call attention to the limitation of idealizations which apply to the overall transport properties of a mixture of fluid and solid particles.Table of Contents1. Introduction.- 1–1 Definition and purpose, 1. 1–2 Historical review, 8. 1–3 Application in science and technology, 13..- 2. The Behavior of Fluids in Slow Motion.- 2–1 The equations of change for a viscous fluid, 23. 2–2 Mechanical energy dissipation in a viscous fluid, 29. 2–3 Force and couple acting on a body moving in a viscous fluid, 30. 2–4 Exact solutions of the equations of motion for a viscous fluid, 31. 2–5 Laminar flow in ducts, 33. 2–6 Simplifications of the Navier-Stokes equations, especially for slow motion, 40. 2–7 Paradoxes in the solution of the creeping motion equations, 47. 2–8 Molecular effects in fluid dynamics, 49. 2–9 Non-newtonian flow, 51. 2–10 Unsteady creeping flows, 52..- 3. Some General Solutions and Theorems Pertaining to the Creeping Motion Equations.- 3–1 Introduction, 58. 3–2 Spherical coordinates, 62. 3–3 Cylindrical coordinates, 71. 3–4 Integral representations, 79. 3–5 Generalized reciprocal theorem, 85. 3–6 Energy dissipation, 88..- 4. Axisymmetrical Flow.- 4–1 Introduction, 96. 4–2 Stream function, 96. 4–3 Relation between stream function and local velocity, 98. 4–4 Stream function in various coordinate systems, 99. 4–5 Intrinsic coordinates, 100. 4–6 Properties of the stream function, 102. 4–7 Dynamic equation satisfied by the stream function, 103. 4–8 Uniform flow, 106. 4–9 Point source or sink, 106. 4–10 Source and sink of equal strength, 107. 4–11 Finite line source, 108. 4–12 Point force, 110. 4–13 Boundary conditions satisfied by the stream function, 111. 4–14 Drag on a body, 113. 4–15 Pressure, 116. 4–16 Separable coordinate systems, 117. 4–17 Translation of a sphere, 119. 4–18 Flow past a sphere, 123. 4–19 Terminal settling velocity, 124. 4–20 Slip at the surface of a sphere, 125. 4–21 Fluid sphere, 127. 4–22 Concentric spheres, 130. 4–23 General solution in spherical coordinates, 133. 4–24 Flow through a conical diffuser, 138. 4–25 Flow past an approximate sphere, 141. 4–26 Oblate spheroid, 145. 4–27 Circular disk, 149. 4–28 Flow in a venturi tube, 150. 4–29 Flow through a circular aperture, 153. 4–30 Prolate spheroid, 154. 4–31 Elongated rod, 156. 4–32 Axisymmetric flow past a spherical cap, 157..- 5. The Motion of a Rigid Particle of Arbitrary Shape in an Unbounded Fluid.- 5–1. Introduction, 159. 5–2 Translational motions, 163. 5–3 Rotational motions, 169. 5–4 Combined translation and rotation, 173. 5–5 Symmetrical particles, 183. 5–6 Nonskew bodies, 192. 5–7 Terminal settling velocity of an arbitrary particle, 197. 5–8 Average resistance to translation, 205. 5–9 The resistance of a slightly deformed sphere, 207. 5–10 The settling of spherically isotropic bodies, 219. 5–11 The settling of orthotopic bodies, 220..- 6. Interaction between Two or More Particles.- 6–1 Introduction, 235. 6–2 Two widely spaced spherically isotropic particles, 240: 6–3 Two spheres by the method of reflections and similar techniques, 249. 6–4 Exact solution for two spheres falling along their line of centers, 270. 6–5 Comparison of theories with experimental data for two spheres, 273. 6–6 More than two spheres, 276. 6–7 Two spheroids in a viscous liquid, 278. 6–8 Limitations of creeping motion equations, 281..- 7. Wall Effects on the Motion of a Single Particle.- 7–1 Introduction, 286. 7–2 The translation of a particle in proximity to container walls, 288. 7–3 Sphere moving in an axial direction in a circular cylindrical tube, 298. 7–4 Sphere moving relative to plane walls, 322. 7–5 Spheroid moving relative to cylindrical and plane walls, 331. 7–6 k-coefficients for typical boundaries, 340. 7–7 One- and two-dimensional problems, 341. 7–8 Solid of revolution rotating symmetrically in a bounded fluid, 346. 7–9 Unsteady motion of a sphere in the presence of a plane wall, 354..- 8. Flow Relative to Assemblages of Particles.- 8–1 Introduction, 358. 8–2 Dilute systems—no interaction effects, 360. 8–3 Dilute systems—first-order interaction effects, 371. 8–4 Concentrated systems, 387. 8–5 Systems with complex geometry, 400. 8–6 Particulate suspensions, 410. 8–7 Packed beds, 417. 8–8 Fluidization, 422..- 9. The Viscosity of Particulate Systems.- 9–1 Introduction, 431. 9–2 Dilute systems of spheres—no interaction effects, 438. 9–3 Dilute systems—first-order interaction effects, 443. 9–4 Concentrated systems, 448. 9–5 Nonspherical and nonrigid particles, 456. 9–6 Comparison with data, 462. 9–7 Non-newtonian behavior, 469..- Appendix A. Orthogonal Curvilinear Coordinate Systems.- A-l Curvilinear coordinates, 474. A-2 Orthogonal curvilinear coordinates, 477. A-3 Geometrical properties, 480. A-4 Differentiation of unit vectors, 481. A-5 Vector differential invariants, 483. A-6 Relations between cartesian and orthogonal curvilinear coordinates, 486. A-7 Dyadics in orthogonal curvilinear coordinates, 488. A-8 Cylindrical coordinate systems, 490. A-9 Circular cylindrical coordinates, 490. A-10 Conjugate cylindrical coordinate systems, 494. A-ll Elliptic cylinder coordinates, 495. A-12 Bipolar cylinder coordinates, 497. A-l3 Parabolic cylinder coordinates, 500. A-14 Coordinate systems of revolution, 501. A-l5 Spherical Coordinates, 504. A-l6 Conjugate coordinate systems of revolution, 508. A-17 Prolate spheroidal coordinates, 509. A-18 Oblate spheroidal coordinates, 512. A-19 Bipolar coordinates, 516. A-20 Toroidal coordinates, 519. A-21 Paraboloidal Coordinates, 521..- Appendix B. Summary of Notation and Brief Review of Polyadic Algebra.- Name Index.

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Book SynopsisThis book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and re­ searchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materi­ als: plasticity, fracture and fatigue, constitutive equations, composite materi­ als, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method. ' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.Trade Review`Professor Mura's book may be heartily recommended to those interested in either applying or learning to apply the methods of continuum mechanics to treat defects in the solid state. This monograph could serve as the perfect text for a second-level graduate course with the same title as that of the book.' Journal of Applied Mechanics Table of Contents1. General theory of eigenstrains.- 1. Definition of eigenstrains.- 2. Fundamental equations of elasticity.- Hooke’s law.- Equilibrium conditions.- Compatibility conditions.- 3. General expressions of elastic fields for given eigenstrain distributions.- Periodic solutions.- Method of Fourier series and Fourier integrals.- Method of Green’s functions.- Isotropic materials.- Cubic crystals.- Hexagonal crystals (transversely isotropic).- 4. Exercises of general formulae.- A straight screw dislocation.- A straight edge dislocation.- Periodic distribution of cuboidal precipitates.- 5. Static Green’s functions.- Isotropic materials.- Anisotropic materials.- Transversely isotropic materials.- Kröner’s formula.- Derivatives of Green’s functions.- Two-dimensional Green’s function.- 6. Inclusions and inhomogeneities.- Inclusions.- Inhomogeneities.- Effect of isotropic elastic moduli on stress.- 7. Dislocations.- Volterra and Mura formulas.- The Indenbom and Orlov formula.- Disclinations.- 8. Dynamic solutions.- Uniformly moving edge dislocation.- Uniformly moving screw dislocation.- 9. Dynamic Green’s functions.- Isotropic materials.- Steady State.- 10. Incompatibility.- Riemann-Christoffel curvature tensor.- 2. Isotropic inclusions.- 11. Eshelby’s solution.- Interior points.- Sphere.- Elliptic cylinder.- Penny-shape.- Flat ellipsoid.- Oblate spheroid.- Prolate spheroid.- Exterior points.- Thermal expansion with central symmetry.- 12. Ellipsoidal inclusions with polynomial eigenstrains.- The I-integrals.- Sphere.- Elliptic cylinder.- Oblate spheroid.- Prolate spheroid.- Elliptical plate.- The Ferrers and Dyson formula.- 13. Energies of inclusions.- Elastic strain energy.- Interaction energy.- Strain energy due to a spherical inclusion.- Elliptic cylinder.- Penny-shaped flat ellipsoid.- Spheroid.- 14. Cuboidal inclusions.- 15. Inclusions in a half space.- Green’s functions.- Ellipsoidal inclusion with a uniform dilatational eigenstrain.- Cuboidal inclusion with uniform eigenstrains.- Periodic distribution of eigenstrains.- Joined half-spaces.- 3. Anisotropic inclusions.- 16. Elastic field of an ellipsoidal inclusion.- 17. Formulae for interior points.- Uniform eigenstrains.- Spheroid.- Cylinder (elliptic inclusion).- Flat ellipsoid.- Eigenstrains with polynomial variation.- Eigenstrains with a periodic form.- 18. Formulae for exterior points.- Examples.- 19. Ellipsoidal inclusions with polynomial eigenstrains in anisotropic media.- Special cases.- 20. Harmonic eigenstrains.- 21. Periodic distribution of spherical inclusions.- 4. Ellipsoidal inhomogeneities.- 22. Equivalent inclusion method.- Isotropic materials.- Sphere.- Penny shape.- Rod.- Anisotropic inhomogeneities in isotropic matrices.- Stress field for exterior points.- 23. Numerical calculations.- Two ellipsoidal inhomogeneities.- 24. Impotent eigenstrains.- 25. Energies of inhomogeneities.- Elastic strain energy.- Interaction energy.- Colunneti’s theorem.- Uniform plastic deformation in a matrix.- Energy balance.- 26. Precipitates and martensites.- Isotropic precipitates.- Anistropic precipitates.- Incoherent precipitates.- Martensitic transformation.- Stress orienting precipitation.- 5. Cracks.- 27. Critical stresses of crakes in isotropic media.- Penny-shaped cracks.- Slit-like cracks.- Flat ellipsoidal cracks.- Crack opening displacement.- 28. Critical stresses of cracks in anisotropic media.- Uniform applied stress.- Non-uniform applied stress.- II integrals for a penny-shaped crack.- II integrals for cubic crystals.- II integrals for transversely isotropic materials.- 29. Stress intensity factor for a flat ellipsoidal crack.- Uniform applied stresses.- Non-uniform applied stresses.- 30. Stress intensity factor for a slit-like crack.- Uniform applied stresses.- Non-uniform applied stresses.- Isotropic materials.- 31. Stress concentration factors.- Simple tension.- Pure shear.- 32. Dugdale-Barenblatt cracks.- BCS model.- Penny shaped crack.- 33. Stress intensity factor for an arbitrarily shaped plane crack.- Numerical examples.- 34. Crack growth.- Energy release rate.- The J-integral.- Fatigue.- Dynamic crack growth.- 6. Dislocations.- 35. Displacement fields.- Parallel dislocations.- A straight dislocation.- 36. Stress fields.- Dislocation segments.- Willis’ formula.- The Asaro et al. formula.- Dislocation loops.- 37. Dislocation density tensor.- Surface dislocation density.- Impotent distribution of dislocations.- 38. Dislocation flux tensor.- Line integral expression of displacement and plastic distortion fields.- The elastic field of moving dislocationswave equations of tensor potentials.- Wave equations of tensor potentials.- 39. Energies and forces.- Dynamic consideration.- 40. Plasticity.- Mathematical theory of plasticity.- Dislocation theory.- Plane strain problems.- Beams and cylinders.- 41. Dislocation model for fatigue crack initiation.- 7. Material properties and related topics.- 42. Macroscopic average.- Average of internal stresses.- Macroscopic strains.- Tanaka-Mori’s theorem.- Image stress.- Random distribution of inclusions-Mori and Tanaka’s theory.- 43. Work-hardening of dispersion hardened alloys.- Work-hardening in simple shear.- Dislocations around an inclusion.- Uniformity of plastic deformation.- 44. Diffusional relaxation of internal and external stresses.- Relaxation of the internal stress in a plastically deformed dispersion strenthened alloy.- Diffusional relaxation process, climb rate of an Orowan loop.- Recovery creep of a dispersion strengthened alloy.- Interfacial diffusional relaxation.- 45. Average elastic moduli of composite materials.- The Voigt approximation.- The Reuss approximation.- Hill’s theory.- Eshelby’s method.- Self-consistent method.- Upper and lower bounds.- Other related works.- 46. Plastic behavior of polycrystalline metals and composites.- Taylor’s analysis.- Self-consistent method.- Embedded weakened zone.- 47. Viscoelasticity of composite materials.- Homogeneous inclusions.- Inhomogeneous inclusions.- Waves in an infinite medium.- 48. Elastic wave scattering.- Dynamic equivalent inclusion method.- Green’s formula.- 49. Interaction between dislocations and inclusions.- Inclusions and dislocations.- Cracks in two-phase materials.- 50. Eigenstrains in lattice theory.- A uniformly moving screw dislocation.- 51. Sliding inclusions.- Shearing Eigenstrains.- Spheroidol inhomogeneous inclusions.- 52. Recent developments.- Inclusions, precipitates, and composites.- Half-spaces.- Non-elastic matrices.- Cracks and inclusions.- Sliding and debonding inclusions.- Dynamic cases.- Miscellaneous.- Appendix 1.- Einstein summation convention.- Kronecker delta.- Permutation tensor.- Appendix 2.- The elastic moduli for isotropic materials.- Appendix 3.- Fourier series and integrals.- Dirac’s delta function and Heaviside’s step function.- Laplace transform.- Appendix 4.- Dislocations pile-up.- References.- Author index.

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Book SynopsisThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.Trade ReviewFrom the reviews:“The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters … . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1172, 2009)Table of ContentsForeword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.

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Book SynopsisThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.Trade ReviewFrom the reviews:“The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters … . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1172, 2009)Table of ContentsForeword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.

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Book SynopsisMicro Electro Mechanical Systems (MEMS) is already about a billion dollars a year industry and is growing rapidly. So far major emphasis has been placed on the fabrication processes for various devices. There are serious issues related to tribology, mechanics, surfacechemistry and materials science in the operationand manufacturingof many MEMS devices and these issues are preventing an even faster commercialization. Very little is understood about tribology and mechanical properties on micro- to nanoscales of the materials used in the construction of MEMS devices. The MEMS community needs to be exposed to the state-of-the-artoftribology and vice versa. Fundamental understanding of friction/stiction, wear and the role of surface contamination and environmental debris in micro devices is required. There are significantadhesion, friction and wear issues in manufacturing and actual use, facing the MEMS industry. Very little is understood about the tribology of bulk silicon and polysilicon films used in the construction ofthese microdevices. These issues are based on surface phenomenaand cannotbe scaled down linearly and these become increasingly important with the small size of the devices. Continuum theory breaks down in the analyses, e. g. in fluid flow of micro-scale devices. Mechanical properties ofpolysilicon and other films are not well characterized. Roughness optimization can help in tribological improvements. Monolayers of lubricants and other materials need to be developed for ultra-low friction and near zero wear. Hard coatings and ion implantation techniques hold promise.Table of ContentsPreface. 1. MEMS Fabrication Techniques. 2. MEMS Applications and Tribology Issues. 3. State-of-the-Art of Tribology: Macroscale Processes. 4. State-of-the-Art of Tribology: Micro- to Nanoscale Processes. 5. Tribology of MEMS Components and Materials. 6. Mechanical Property Measurements. 7. Modification and Characterization of Surfaces. 8. Breakout Sessions Report. 9. Panel Discussion Report. List of Participants. Subject Index. Editor's Vita.

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Book SynopsisThis textbook covers all fundamental concepts of physics and describes how different theories are developed from physical observations and phenomena. After some essential calculus the author presents the complete classical mechanics giving numerous examples and with a clear focus on problem-solving techniques. Due to the high number of exercises at the end of each chapter and their solutions the work is valuable for self-study.

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Book SynopsisThe work shows, by means of examples coming from different corners of physics, how physical and mathematical questions can be answered using a computer. Starting with maps and neural networks, applications from Newton's mechanics described by ordinary differential equations come into the focus, like the computation of planetary orbits or classical molecular dynamics. A large part of the textbook is dedicated to deterministic chaos normally encountered in systems with sufficiently many degrees of freedom. Partial differential equations are studied considering (nonlinear) field theories like quantum mechanics, thermodynamics or fluid mechanics. In the second edition, a new chapter gives a detailed survey on delay or memory systems with a direct application to epidemic and road traffic models. Most of the algorithms are realized in FORTRAN, a language most suitable for effectively solving the discussed problems. On the other hand, the codes given and presented on the book’s homepage can be easily translated into other languages. Moreover, several MATLAB examples are presented, mainly for didactic reasons. The book is addressed to advanced Bachelor or Master students of physics, applied mathematics and mechanical engineering.

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Book SynopsisThis book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This approach allows students to solve more advanced and applied problems at an earlier stage and equips them to deal with real-world examples well beyond the typical special cases treated in standard textbooks.Another advantage of this approach is that students are brought closer to the way physics is actually discovered and applied, as they are introduced right from the start to a more exploratory way of understanding phenomena and of developing their physical concepts.While not a requirement, it is advantageous for the reader to have some prior knowledge of scientific programming with a scripting-type language. This edition of the book uses Python, and a chapter devoted to the basics of scientific programming with Python is included. A parallel edition using Matlab instead of Python is also available.Last but not least, each chapter is accompanied by an extensive set of course-tested exercises and solutions.Table of ContentsIntroduction.- Getting started with programming.- Units and measurement.- Motion in one dimension.- Forces in one dimension.- Motion in two and three dimensions.- Forces in two and three dimensions.- Constrained motion.- Forces and constrained motion.- Work.- Energy.- Momentum, impulse, and collisions.- Multiparticle systems.- Rotational motion.- Rotation of rigid bodies.- Dynamics of rigid bodies.- Proofs.- Solutions.- Index.

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Book SynopsisThis book addresses a range of basic and essential topics, selected from the author's teaching and research activities, offering a comprehensive guide in three parts: Statics, Kinematics and Kinetics. Chapter 1 briefly discusses the history of classical and modern mechanics, while Chapter 2, presents preliminary knowledge, preparing readers for the subsequent chapters. Chapters 3 to 7 introduce statics, force analysis, simplification of force groups, equilibrium of the general coplanar force group, and the center of the parallel force group. The Kinematics section (Chapters 8 to 10), covers the motion of a particle, basic motion and planar motion of a rigid body.Lastly, the Kinetics section (Chapters 11 to 14) explores Newton’s law of motion, theorem of momentum, theorem of angular momentum, and theorem of kinetic energy. With numerous examples from engineering, illustrations, and step-by-step tutorials, the book is suitable for both classroom use and self-study. After completing the course, students will be able to simplify complex engineering structures and perform force and motion analyses on particles and structures, preparing them for further study and research. The book can be used as a textbook for undergraduate courses on fundamental aspects of theoretical mechanics, such as aerospace, mechanical engineering, petroleum engineering, automotive and civil engineering, as well as material science and engineering.Table of ContentsPreface.- Preliminary knowledge.- Fundamentals of statics.- Force analysis.- Simplification of a force group.- Equilibrium of the general coplanar force gruop.- Center of the parallel force group.- Motion of a particle.- Basic motion of the rigid body.- Planar motion of the rigid body.- Newton’s laws of motion.- Theorem of momentum.- Theorem of angular momentum.- Theorem of kinetic energy.- Summary.

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