1  20
Next
 Bestehorn, Michael, 1957 author.
 Berlin ; Boston : De Gruyter, [2018]
 Description
 Book — 1 online resource (330 p). Digital: text file; PDF.
 Summary

 Frontmatter
 Contents
 1. Introduction
 2. Nonlinear maps
 3. Dynamical systems
 4. Ordinary differential equations I, initial value problems
 5. Ordinary differential equations II, boundary value problems
 6. Partial differential equations I, basics
 7. Partial differential equations II, applications
 8. Monte Carlo methods (MC)
 A. Matrices and systems of linear equations
 B. Program library
 C. Solutions of the problems
 D. README and a short guide to FEtools
 Index
(source: Nielsen Book Data)
2. Engineering mechanics [2022]
 Yi, Ping, author.
 [Place of publication not identified] : EDP Sciences & Science Press, [2022]
 Description
 Book — 1 online resource : illustrations (some color).
 Summary

 Frontmatter
 Foreword
 Contents
 Chapter 1. Introduction
 Chapter 2. Vectors and Vector Operations
 Chapter 3. Simplification of Force Systems
 Chapter 4. Equilibrium of Rigid Bodies
 Chapter 5. Friction
 Chapter 6. Kinematics of Particles
 Chapter 7. Planar Kinematics of Rigid Bodies
 Chapter 8. Kinetics: Equations of Motion
 Chapter 9. Kinetics: Work and Energy
 Chapter 10. Kinetics: Impulse and Momentum
 Answers
 References
3. Rigid Body Dynamics [2018]
 Borisov, Alexey, author.
 Berlin ; Boston : De Gruyter, [2018]
 Description
 Book — 1 online resource (533 p). Digital: text file; PDF.
 Summary

 Frontmatter
 Contents
 Introduction
 The Creators of Rigid Body Dynamics
 1. Rigid Body Equations of Motion and Their Integration
 2. The Euler  Poisson Equations and Their Generalizations
 3. The Kirchhoff Equations and Related Problems of Rigid Body Dynamics
 4. Linear Integrals and Reduction
 5. Generalizations of Integrability Cases. Explicit Integration
 6. Periodic Solutions, Nonintegrability, and Transition to Chaos
 A. Derivation of the Kirchhoff, Poincaré  Zhukovskii, and FourDimensional Top Equations
 B. The Lie Algebra e(4) and Its Orbits
 C. Quaternion Equations and LA Pair for the Generalized Goryachev  Chaplygin Top
 D. The Hess Case and Quantization of the Rotation Number
 E. Ferromagnetic Dynamics in a Magnetic Field
 F. The Landau  Lifshitz Equation, Discrete Systems, and the Neumann Problem
 G. Dynamics of Tops and Material Points on Spheres and Ellipsoids
 H. On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation
 I. The Hamiltonian Dynamics of Selfgravitating Fluid and Gas Ellipsoids
 Bibliography
 Index of Names
 Index
(source: Nielsen Book Data)
 Zain, Samya, author.
 Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]
 Description
 Book — 1 online resource (various pagings) : illustrations (some color).
 Summary

 1. Foundations
 1.1. The nature of science
 1.2. Units
 1.3. International system of units (SI)
 1.4. Dimensional analysis
 1.5. A quick review of vectors
 1.6. Derivatives of vectors
 1.7. Position vector
 1.8. Transformation between various coordinate systems
 1.9. Velocity and acceleration
 1.10. Velocity and acceleration in various coordinates
 2. Conservation laws
 2.1. Introduction
 2.2. Conservation laws
 2.3. Forces that depend on position : energy considerations
 2.4. Onedimensional conservative system : complete solution
 3. Newtonian mechanics
 3.1. Introduction
 3.2. Rectilinear motion under uniform acceleration
 3.3. Linear momentum
 3.4. Newton's laws of motion
 3.5. Torque
 4. Lagrangian mechanics
 4.1. Lagrangian mechanics
 4.2. From Newtonian to Lagrangian formalism
 4.3. Choosing Lagrange's formalismwhen and where?
 4.4. Lagrangian formalism for nonconservative forces
 4.5. The Lagrangian formalism in a nutshell
 5. Hamiltonian mechanics
 5.1. Hamiltonian mechanics
 5.2. The Hamiltonian principle
 5.3. Classical and quantum mechanics
 6. Waves and oscillations
 6.1. Mechanical waves
 6.2. Physical properties of waves
 6.3. Standing waves
 6.4. Resonance
 7. Simple harmonic oscillation
 7.1. Harmonic oscillator
 7.2. Energy consideration in harmonic oscillator
 7.3. About various pendulums
 7.4. Simple gravity pendulum
 7.5. Elastic pendulum
 7.5..1 Elastic pendulumLagrangian mechanics
 7.6. Spherical pendulum
 8. Gravitation and central forces
 8.1. Introduction
 8.2. Newton's law of universal gravitation
 8.3. Gravity
 8.4. Gravitational force between a uniform sphere and a particle
 8.5. Potential energy in a gravitational field : gravitational potential
 8.6. Kepler's law of planetary motion
 9. Two and threedimensional dynamics
 9.1. Introduction : general principles
 9.2. Some useful mathematical concepts
 9.3. Conservative and nonconservative forces in 3D
 9.4. Generalized conservation of energy principle in 3D
 9.5. The energy equation
 9.6. Body with variable mass
 10. Circular and projectile motion
 10.1. Motion in higher dimensions
 10.2. Uniform circular motion
 10.3. Rotational motion
 10.4. Rectilinear motion and rotation about a fixed axis
 10.5. Harmonic oscillator in higher dimensions
 10.6. Motion of a projectile in a uniform gravitational field
 10.7. Projectile motion : no air resistance
 11. Fluidstatics
 11.1. Types of materials
 11.2. Fluidstatics
 11.3. Pressure and density in fluidstatistics
 11.4. Pressure in fluidstatistics
 11.5. Archimedes' principle
 11.6. Specific gravity
 11.7. Pascal's principle
 11.8. Center of buoyancy
 12. Fluid resistance
 12.1. Fluid resistance
 12.2. Forces as a function of velocity : fluid resistance
 12.3. A falling object under linear drag
 12.4. Falling object : the quadratic case
 12.5. Projectile motion : air resistance
 12.6. Damped harmonic oscillator in 1D
 13. Fluid dynamics
 13.1. Fluid dynamics
 13.2. Fluid flow
 13.3. Viscosity
 13.4. Bernoulli's principle
 13.5. Velocity of the fall of a sphere through a viscous liquid
 13.6. Turbulent motion and Reynolds number
 14. Properties of solids
 14.1. Solids
 14.2. Stress
 14.3. Strain
 14.4. Waves in solids
 15. Rotationmotion of rigid bodies
 15.1. Rigid bodies
 15.2. Moment of inertia
 15.3. Mass on an incline
 15.4. Laminar motion of a rigid body
 16. System of particles
 16.1. System of particles
 16.2. Twoparticle system
 16.3. Manyparticle systems
 16.4. Conservation of momentum in a system of
 16.5. Collisions
 16.6. 1D collision in the centerofmomentum reference frame
 17. Scattering theory
 17.1. Crosssection
 17.2. Types of scattering
 17.3. Neutral crosssection
 17.4. Capture crosssection
 17.5. Repulsive crosssection
 17.6. Scattering of alpha particles
 Appendices. A. Unit conversion
 B. Velocity and acceleration in various coordinates
 C. Noether's theorem
 D. Configuration space.
 Sharipov, Felix, author.
 Weinheim, Germany : WileyVCH, [2015].
 Description
 Book — 1 online resource.
 Summary

 Preface XIII List of Symbols XV List of Acronyms XXI 1 Molecular Description 1 1.1 Mechanics of Continuous Media and Its Restriction 1 1.2 Macroscopic State Variables 2 1.3 Dilute Gas 3 1.4 Intermolecular Potential 4 1.4.1 Definition of Potential 4 1.4.2 Hard Sphere Potential 4 1.4.3 LennardJones Potential 5 1.4.4 Ab initio Potential 5 1.5 Deflection Angle 7 1.6 Differential Cross
 Section 8 1.7 Total Cross
 Section 9 1.8 Equivalent Free Path 10 1.9 Rarefaction Parameter and Knudsen Number 10 2 Velocity Distribution Function 13 2.1 Definition of Distribution Function 13 2.2 Moments of Distribution Function 15 2.3 Entropy and Its Flow Vector 18 2.4 Global Maxwellian 18 2.5 Local Maxwellian 20 3 Boltzmann Equation 23 3.1 Assumptions to Derive the Boltzmann Equation 23 3.2 General Form of the Boltzmann Equation 23 3.3 Conservation Laws 25 3.4 Entropy Production due to Intermolecular Collisions 27 3.5 Intermolecular Collisions Frequency 27 4 GasSurface Interaction 31 4.1 General form of Boundary Condition for Impermeable Surface 31 4.2 DiffuseSpecular Kernel 33 4.3 CercignaniLampis Kernel 34 4.4 Accommodation Coefficients 34 4.5 General form of Boundary Condition for Permeable Surface 37 4.6 Entropy Production due to GasSurface Interaction 38 5 Linear Theory 43 5.1 Small Perturbation of Equilibrium 43 5.2 Linearization Near Global Maxwellian 43 5.3 Linearization Near Local Maxwellian 46 5.4 Properties of the Linearized Collision Operator 47 5.5 Linearization of Boundary Condition 48 5.5.1 Impermeable Surface Being at Rest 48 5.5.2 Impermeable Moving Surface 49 5.5.3 Permeable Surface 50 5.5.4 Linearization Near Reference Maxwellian 50 5.5.5 Properties of Scattering Operator 50 5.5.6 Diffuse Scattering 51 5.6 Series Expansion 51 5.7 Reciprocal Relations 53 5.7.1 General Definitions 53 5.7.2 Kinetic Coefficients 54 6 Transport Coefficients 57 6.1 Constitutive Equations 57 6.2 Viscosity 58 6.3 Thermal Conductivity 59 6.4 Numerical Results 61 6.4.1 Hard Sphere Potential 61 6.4.2 LennardJones Potential 61 6.4.3 Ab Initio Potential 62 7 Model Equations 65 7.1 BGK Equation 65 7.2 SModel 67 7.3 Ellipsoidal Model 69 7.4 Dimensionless Form of Model Equations 70 8 Direct Simulation Monte Carlo Method 73 8.1 Main Ideas 73 8.2 Generation of Specific Distribution Function 74 8.3 Simulation of GasSurface Interaction 75 8.3.1 Kernel Decomposition 75 8.3.2 Diffuse Scattering 75 8.3.3 CercignaniLampis Scattering 76 8.4 Intermolecular Interaction 77 8.5 Calculation of PostCollision Velocities 78 8.6 Calculation of Macroscopic Quantities 80 8.7 Statistical Scatter 81 9 Discrete Velocity Method 83 9.1 Main Ideas 83 9.2 Velocity Discretization 85 9.2.1 Onefold Integral 85 9.2.2 Twofold Integral 86 9.3 Iterative Procedure 87 9.4 Finite Difference Schemes 88 9.4.1 Main Principles 88 9.4.2 OneDimensional Planar Flows 89 9.4.3 TwoDimensional Planar Flows 90 9.4.4 OneDimensional Axisymmetric Flows 93 9.4.5 Full Kinetic Equation 96 10 Velocity Slip and Temperature Jump Phenomena 97 10.1 General Remarks 97 10.2 Viscous Velocity Slip 98 10.2.1 Definition and Input Equation 98 10.2.2 Velocity and Heat Flow Profiles 100 10.2.3 Numerical and Experimental Data 101 10.3 Thermal Velocity Slip 104 10.3.1 Definition and Input Equation 104 10.3.2 Velocity and Heat Flow Profiles 106 10.3.3 Numerical and Experimental Data 107 10.4 Reciprocal Relation 108 10.5 Temperature Jump 110 10.5.1 Definition and Input Equation 110 10.5.2 Temperature Profile 112 10.5.3 Numerical Data 112 11 OneDimensional Planar Flows 115 11.1 Planar Couette Flow 115 11.1.1 Definitions 115 11.1.2 FreeMolecular Regime 116 11.1.3 Velocity Slip Regime 117 11.1.4 Kinetic Equation 117 11.1.5 Numerical Scheme 119 11.1.6 Numerical Results 120 11.2 Planar Heat Transfer 121 11.2.1 Definitions 121 11.2.2 FreeMolecular Regime 122 11.2.3 Temperature Jump Regime 123 11.2.4 Kinetic Equation 124 11.2.5 Numerical Scheme 126 11.2.6 Numerical Results 127 11.3 Planar Poiseuille andThermal Creep Flows 128 11.3.1 Definitions 128 11.3.2 Slip Solution 130 11.3.3 Kinetic Equation 131 11.3.4 Reciprocal Relation 133 11.3.5 Numerical Scheme 133 11.3.6 Splitting Scheme 134 11.3.7 FreeMolecular Limit 137 11.3.8 Numerical Results 137 12 OneDimensional Axisymmetrical Flows 145 12.1 Cylindrical Couette Flow 145 12.1.1 Definitions 145 12.1.2 Slip Flow Regime 146 12.1.3 Kinetic Equation 147 12.1.4 FreeMolecular Regime 148 12.1.5 Numerical Scheme 149 12.1.6 Splitting Scheme 150 12.1.7 Results 152 12.2 Heat Transfer between Two Cylinders 153 12.2.1 Definitions 153 12.2.2 Temperature Jump Solution 154 12.2.3 Kinetic Equation 155 12.2.4 FreeMolecular Regime 156 12.2.5 Numerical Scheme 157 12.2.6 Splitting Scheme 158 12.2.7 Numerical Results 159 12.3 Cylindrical Poiseuille andThermal Creep Flows 161 12.3.1 Definitions 161 12.3.2 Slip Solution 163 12.3.3 Kinetic Equation 163 12.3.4 Reciprocal Relation 165 12.3.5 FreeMolecular Regime 165 12.3.6 Numerical Scheme 166 12.3.7 Results 168 13 TwoDimensional Planar Flows 173 13.1 Flows Through a Long Rectangular Channel 173 13.1.1 Definitions 173 13.1.2 Slip Solution 174 13.1.3 Kinetic Equation 175 13.1.4 FreeMolecular Regime 177 13.1.5 Numerical Scheme 177 13.1.6 Numerical Results 178 13.2 Flows Through Slits and Short Channels 180 13.2.1 Formulation of the Problem 180 13.2.2 FreeMolecular Regime 181 13.2.3 Small Pressure and Temperature Drops 183 13.2.3.1 Definitions 183 13.2.3.2 Kinetic Equation 184 13.2.3.3 Hydrodynamic Solution 186 13.2.3.4 Numerical Results 186 13.2.4 Arbitrary Pressure Drop 189 13.2.4.1 Definition 189 13.2.4.2 Kinetic Equation 189 13.2.4.3 Numerical Results 190 13.3 End Correction for Channel 194 13.3.1 Definitions 194 13.3.2 Kinetic Equation 196 13.3.3 Numerical Results 197 14 TwoDimensional Axisymmetrical Flows 201 14.1 Flows Through Orifices and Short Tubes 201 14.1.1 Formulation of the Problem 201 14.1.2 FreeMolecular Flow 202 14.1.3 Small Pressure Drop 203 14.1.3.1 Definitions 203 14.1.3.2 Kinetic Equations 204 14.1.3.3 Hydrodynamic Solution 205 14.1.3.4 Numerical Results 205 14.1.4 Arbitrary Pressure Drop 206 14.2 End Correction for Tube 210 14.2.1 Definitions 210 14.2.2 Numerical Results 212 14.3 Transient Flow Through a Tube 213 15 Flows Through Long Pipes Under Arbitrary Pressure and Temperature Drops 219 15.1 Stationary Flows 219 15.1.1 Main Equations 219 15.1.2 Isothermal Flows 221 15.1.3 Nonisothermal Flows 223 15.2 Pipes with Variable Cross
 Section 224 15.3 Transient Flows 226 15.3.1 Main Equations 226 15.3.2 Approaching to Equilibrium 227 16 Acoustics in Rarefied Gases 231 16.1 General Remarks 231 16.1.1 Description ofWaves in Continuous Medium 231 16.1.2 Complex Perturbation Function 232 16.1.3 OneDimensional Flows 233 16.2 Oscillatory Couette Flow 234 16.2.1 Definitions 234 16.2.2 Slip Regime 235 16.2.3 Kinetic Equation 237 16.2.4 FreeMolecular Regime 238 16.2.5 Numerical Scheme 239 16.2.6 Numerical Results 241 16.3 LongitudinalWaves 242 16.3.1 Definitions 242 16.3.2 Hydrodynamic Regime 244 16.3.3 Kinetic Equation 246 16.3.4 Reciprocal Relation 249 16.3.5 HighFrequency Regime 250 16.3.6 Numerical Results 252 A Constants and Mathematical Expressions 257 A.1 Physical Constants 257 A.2 Vectors and Tensors 257 A.3 Nabla Operator 259 A.4 Kronecker Delta and Dirac Delta Function 259 A.5 Some Integrals 260 A.6 Taylor Series 260 A.7 Some Functions 260 A.8 GaussOstrogradsky'sTheorem 262 A.9 Complex Numbers 262 B Files and Listings 263 B.1 Files with Nodes andWeights of Gauss Quadrature 263 B.1.1 Weighting Function (9.16) 263 B.1.1.1 File cw4.dat, Nc = 4 263 B.1.1.2 File cw6.dat, Nc = 6 263 B.1.1.3 File cw8.dat, Nc = 8 263 B.1.2 Weighting Function (9.22) 264 B.1.2.1 File cpw4.dat, Nc = 4 264 B.1.2.2 File cpw6.dat, Nc = 6 264 B.1.2.3 File cpw8.dat, Nc = 8 264 B.2 Files for Planar Couette Flow 264 B.2.1 Listing of Program "couette_planar.for" 264 B.2.2 Output File with Results "Res_couette_planar.dat" 266 B.3 Files for Planar Heat Transfer 266 B.3.1 Listing of Program "heat_planar.for" 266 B.3.2 Output File with Results "Res_heat_planar.dat" 268 B.4 Files for Planar Poiseuille and Creep Flows 268 B.4.1 Listing of Program "poiseuille_creep_planar.for" 268 B.4.2 Output File "Res_pois_cr_pl.dat" with Results 272 B.5 Files for Cylindrical Couette Flows 272 B.5.1 Listing of Program "couette_axisym.for" 272 B.5.2 Output File "Res_couet_axi.dat" with Results 275 B.6 Files for Cylindrical Heat Transfer 276 B.6.1 Listing of Program "heat_axisym.for" 276 B.6.2 Output File "Res_heat_axi.dat" with Results 280 B.7 Files for AxiSymmetric Poiseuille and Creep Flows 280 B.7.1 Listing of Program "poiseuille_creep_axisym.for" 280 B.7.2 Output File "Res_pois_cr_axi.dat" with Results 284 B.8 Files for Poiseuille and Creep FlowsThrough Channel 284 B.8.1 Listing of Program "poiseuille_creep_chan.for" 284 B.8.2 Output File "Res_pois_cr_ch.dat" with Results 287 B.9 Files for Oscillating Couette Flow 287 B.9.1 Listing of Program "couette_osc.for" 287 B.9.2 Output File "Res_couette_osc.dat" with Results 290 References 291 Index 303.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 International Symposium on Rarefied Gas Dynamics (8th : 1972 : Stanford University)
 New York ; London : Academic Press, 1974.
 Description
 Book — 1 online resource (xix, 541 p.) : ill.
 Likharev, K. K. (Konstantin Konstantinovich), author.
 Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018]
 Description
 Book — 1 online resource (various pagings) : illustrations (some color).
 Summary

 1. Review of fundamentals
 2. Lagrangian analytical mechanics
 3. A few simple problems
 4. Rigidbody motion
 5. Oscillations
 6. From oscillations to waves
 7. Deformations and elasticity
 8. Fluid mechanics
 9. Deterministic chaos
 10. A bit more of analytical mechanics
 Appendices. A. Selected mathematical formulas
 B. Selected physical constants.
 Berlin ; Boston : De Gruyter, [2019]
 Description
 Book — 1 online resource (370 p.) Digital: text file; PDF.
 Summary

 Frontmatter
 Preface
 Contents
 General Scheme of Notations
 1. Introduction
 2. Geometry of Physical Space
 3. Essentials of NonLinear Elasticity Theory
 4. Geometric Formalization of the Body and Its Representation in Physical Space
 5. Strain Measures
 6. Motion
 7. Stress Measures
 8. Material Uniformity and Inhomogeneity
 9. Material Connections
 10. Balance Equations
 11. The Evolutionary Problem  Examples
 12. Algebraic Structures
 13. Review of Smooth Manifolds and Vector Bundles
 14. Connections on Principal Bundles
 Bibliography
 Index
(source: Nielsen Book Data)
9. Classical mechanics : lecture notes [2017]
 Likharev, K. K. (Konstantin Konstantinovich), author.
 Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2017]
 Description
 Book — 1 online resource (various pagings) : illustrations (chiefly color).
 Summary

 1. Review of fundamentals
 1.1. Kinematics : basic notions
 1.2. Dynamics : Newton's laws
 1.3. Conservation laws
 1.4. Potential energy and equilibrium
 1.5. OK, we've got itcan we go home now?
 1.6. Problems
 2. Lagrangian analytical mechanics
 2.1. Lagrange equations
 2.2. Three simple examples
 2.3. Hamiltonian function and energy
 2.4. Other conservation laws
 2.5. Problems
 3. A few simple problems
 3.1. Onedimensional and 1Dreducible systems
 3.2. Equilibrium and stability
 3.3. Hamiltonian 1D systems
 3.4. Planetary problems
 3.5. Elastic scattering
 3.6. Problems
 4. Rigidbody motion
 4.1. Translation and rotation
 4.2. Inertia tensor
 4.3. Fixedaxis rotation
 4.4. Free rotation
 4.5. Torqueinduced precession
 4.6. Noninertial reference frames
 4.7. Problems
 5. Oscillations
 5.1. Free and forced oscillations
 5.2. Weakly nonlinear oscillations
 5.3. Reduced equations
 5.4. Selfoscillations and phaselocking
 5.5. Parametric excitation
 5.6. Fixedpoint classification
 5.7. Numerical approaches
 5.8. Higher harmonic and subharmonic oscillations
 5.9. Problems
 6. From oscillations to waves
 6.1. Two coupled oscillators
 6.2. N coupled oscillators
 6.3. 1D waves
 6.4. Acoustic waves
 6.5. Standing waves
 6.6. Wave decay and attenuation
 6.7. Nonlinear and parametric effects
 6.8. Problems
 7. Deformations and elasticity
 7.1. Strain
 7.2. Stress
 7.3. Hooke's law
 7.4. Equilibrium
 7.5. Rod bending
 7.6. Rod torsion
 7.7. 3D acoustic waves
 7.8. Elastic waves in restricted geometries
 7.9. Problems
 8. Fluid mechanics
 8.1. Hydrostatics
 8.2. Surface tension effects
 8.3. Kinematics
 8.4. Dynamics : ideal fluids
 8.5. Dynamics : viscous fluids
 8.6. Turbulence
 8.7. Problems
 9. Deterministic chaos
 9.1. Chaos in maps
 9.2. Chaos in dynamic systems
 9.3. Chaos in Hamiltonian systems
 9.4. Chaos and turbulence
 9.5. Problems
 10. A bit more of analytical mechanics
 10.1. Hamilton equations
 10.2. Adiabatic invariance
 10.3. The Hamilton principle
 10.4. The HamiltonJacobi equation
 10.5. Problems
 Appendices. A. Selected mathematical formulas
 B. Selected physical constants.
 Sussman, Gerald Jay.
 [Second edition].  Cambridge, MA : The MIT Press, 2015.
 Description
 Book — 1 online resource.
 Summary

The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation. We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic. It weaves recent discoveries in nonlinear dynamics throughout the text, rather than presenting them as an afterthought. Explorations of phenomena such as the transition to chaos, nonlinear resonances, and resonance overlap to help the student develop appropriate analytic tools for understanding. The book uses computation to constrain notation, to capture and formalize methods, and for simulation and symbolic analysis. The requirement that the computer be able to interpret any expression provides the student with strict and immediate feedback about whether an expression is correctly formulated. This second edition has been updated throughout, with revisions that reflect insights gained by the authors from using the text every year at MIT. In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.
(source: Nielsen Book Data)
 Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2020]
 Description
 Book — 1 online resource (various pagings) : illustrations (some color)
 Summary

 6. Centre of mass and collisions
 6.1. The centre of mass
 6.2. Collisions
 7. Orbits
 7.1. Orbital forces
 7.2. Circular motion approximation
 7.3. Motion under the inverse square law of force
 7.4. Orbits under an attractive force : elliptical orbits and Kepler's laws
 7.5. Orbits with positive energy : unbound orbits
 7.6. Reduced mass and the twobody problem
 7.7. Variable mass problems
 8. Rigid bodies
 8.1. Preliminaries
 8.2. Centre of mass
 8.3. Flat object in xy plane
 8.4. General motion of a nonplanar object in 3D space
 9. Accelerating frames of reference
 9.1. Fictitious forces
 10. Fluid mechanics
 10.1. Hydrostatics
 10.2. Hydrodynamicsfluids in motion
 11. Solutions to chapter 1 : mathematical preliminaries
 12. Solutions to chapter 2 : Newton's laws
 13. Selected solutions to chapter 3 : kinematic relations
 14. Selected solutions to chapter 4 : oscillatory motion
 15. Selected solutions to chapter 5 : angular momentum and central forces
 16. Solutions to chapter 6 : centre of mass and collisions
 17. Solutions to chapter 7 : orbits
 18. Selected solutions to chapter 8 : rigid bodies
 19. Selected solutions to chapter 9 : accelerating frames of reference
 20. Solutions to chapter 10 : fluid mechanics
 1. Mathematical preliminaries
 1.1. Vectors
 1.2. Complex numbers
 1.3. Calculus
 1.4. Differential equations
 2. Newton's laws
 2.1. Newton's laws of motion
 2.2. The concept of force
 2.3. Motion under a constant force
 2.4. Projectiles
 2.5. Momentum and impulse
 2.6. Conservation of momentum for isolated systems
 3. Kinematic relations
 3.1. Work and energy
 3.2. Relationship between work and kinetic energy
 3.3. Power
 3.4. Potential energy and conservative forces
 4. Oscillatory motion
 4.1. Simple harmonic motion
 4.2. Damped harmonic motion
 4.3. Driven and damped harmonic motion
 4.4. Coupled oscillators
 5. Angular momentum and central forces
 5.1. Polar coordinates
 5.2. Circular motion
 5.3. Angular momentum
 5.4. Central forces
 Pert, G. J. (Geoffrey J.)
 Chichester, West Sussex, United Kingdom : John Wiley & Sons Ltd., [2013]
 Description
 Book — xx, 468 pages : illustrations ; 26 cm
 Summary

 Preface xvii
 1 Introduction 1
 2 Flow of Ideal Fluids 25
 3 Viscous Fluids 75
 4 Waves and Instabilities in Fluids 93
 5 Turbulent Flow 117
 6 Boundary Layer Flow 139
 7 Convective Heat Transfer 175
 8 Compressible Flow and Sound Waves 209
 9 Characteristics and Rarefactions 219
 10 Shock Waves 241
 11 Aerofoils in LowSpeed Incompressible Flow 295
 12 Aerofoils in HighSpeed Compressible Fluid Flow 341
 13 Deflagrations and Detonations 363
 14 Selfsimilar Methods in Compressible Gas Flow and Intermediate Asymptotics 383 Problems 417 Solutions 427 Bibliography 455 Index 463.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QC145.2 .P47 2013  Unknown 
 Borel, Michel, author.
 London, United Kingdom : ISTE, Ltd. ; Hoboken, NJ : Wiley, 2017.
 Description
 Book — 1 online resource.
 Summary

 Introduction xi Table of Notations xiii Chapter 1. Vector Calculus 1 1.1. Vector space 1 1.1.1. Definition 1 1.1.2. Vector space  dimension  basis 2 1.1.3. Affine space 3 1.2. Affine space of dimension 3  free vector 4 1.3. Scalar product aâ b 5 1.3.1. Properties of the scalar product 6 1.3.2. Scalar square  unit vector 6 1.3.3. Geometric interpretation of the scalar product 7 1.3.4. Solving the equation a
 â x
 = 0 9 1.4. Vector product a â § b 9 1.4.1. Definition 9 1.4.2. Geometric interpretation of the vector product 10 1.4.3. Properties of vector product 11 1.4.4. Solving the equation a â § x = b 11 1.5. Mixed product (a , b, c ) 12 1.5.1. Definition 12 1.5.2. Geometric interpretation of the mixed product 12 1.5.3. Properties of the mixed product 13 1.6. Vector calculus in the affine space of dimension 3 15 1.6.1. Orthonormal basis 15 1.6.2. Analytical expression of the scalar product 16 1.6.3. Analytical expression of the vector product 16 1.6.4. Analytical expression of the mixed product 17 1.7. Applications of vector calculus 18 1.7.1. Double vector product 18 1.7.2. Resolving the equation a
 â x
 = b 22 1.7.3. Resolving the equation a â § x = b 23 1.7.4. Equality of Lagrange 25 1.7.5. Equations of planes 25 1.7.6. Relations within the triangle 27 1.8. Vectors and basis changes 28 1.8.1. Einstein's convention 28 1.8.2. Transition table from basis (e) to basis (E) 30 1.8.3. Characterization of the transition table 32 Chatper 2. Torsors and Torsor Calculus 35 2.1. Vector sets 35 2.1.1. Discrete set of vectors 35 2.1.2. Set of vectors defined on a continuum 36 2.2. Introduction to torsors 37 2.2.1. Definition 37 2.2.2. Equivalence of vector families 38 2.3. Algebra torsors 38 2.3.1. Equality of two torsors 38 2.3.2. Linear combination of torsors 39 2.3.3. Null torsors 39 2.3.4. Opposing torsor 40 2.3.5. Product of two torsors 40 2.3.6. Scalar moment of a torsor  equiprojectivity 41 2.3.7. Invariant scalar of a torsor 43 2.4. Characterization and classification of torsors 43 2.4.1. Torsors with a null resultant 43 2.4.2. Torsors with a nonull resultant 45 2.5. Derivation torsors 48 2.5.1. Torsor dependent on a single parameter q 49 2.5.2. Torsor dependent of n parameters qi functions of p 51 2.5.3. Explicitly dependent torsor of n + 1 parameters 52 Chapter 3. Derivation of Vector Functions 55 3.1. Derivative vector: definition and properties 55 3.2. Derivative of a function in a basis 56 3.3. Deriving a vector function of a variable 57 3.3.1. Relations between derivatives of a function in different bases 57 3.3.2. Differential form associated with two bases 63 3.4. Deriving a vector function of two variables 65 3.5. Deriving a vector function of n variables 68 3.6. Explicit intervention of the variable p 70 3.7. Relative rotation rate of a basis relative to another 71 Chapter 4. Vector Functions of One Variable Skew Curves 73 4.1. Vector function of one variable 73 4.2. Tangent at a point M 74 4.3. Unit tangent vector Ï ( q) 76 4.4. Main normal vector ( ) q Î½ 77 4.5. Unit binormal vector ( ) q ss 79 4.6. Frenet's basis 80 4.7. Curvilinear abscissa 81 4.8. Curvature, curvature center and curvature radius 83 4.9. Torsion and torsion radius 84 4.10. Orientation in (Î») of the Frenet basis 87 Chapter 5. Vector Functions of Two Variables Surfaces 91 5.1. Representation of a vector function of two variables 91 5.1.1. Coordinate curves 91 5.1.2. Regular or singular point  tangent plane  unit normal vector 93 5.1.3. Distinctive surfaces 95 5.1.4. Ruled surfaces 101 5.1.5. Area element 110 5.2. General properties of surfaces 111 5.2.1. First quadratic form 111 5.2.2. DarbouxRibaucour's trihedral 114 5.2.3. Second quadratic form 119 5.2.4. Meusnier's theorems 121 5.2.5. Geodesic torsion 123 5.2.6. Prominent curves traced on a surface 125 5.2.7. Directions and principal curvatures of a surface 127 Chapter 6. Vector Function of Three Variables: Volumes 135 6.1. Vector functions of three variables 135 6.1.1. Coordinate surfaces 135 6.1.2. Coordinate curves 136 6.1.3. Orthogonal curvilinear coordinates 136 6.2. Volume element 137 6.2.1. Definition 137 6.2.2. Applications to traditional coordinate systems 138 6.3. Rotation rate of the local basis 139 6.3.1. Calculation of the partial rotation rate 1Î´ (Î» , e) 140 6.3.2. Calculation of the rotation rate 143 Chapter 7. Linear Operators 145 7.1. Definition 145 7.2. Intrinsic properties 145 7.3. Algebra of linear operators 147 7.3.1. Unit operator 147 7.3.2. Equality of two linear operators 147 7.3.3. Product of a linear operator by a scalar 147 7.3.4. Sum of two linear operators 148 7.3.5. Multiplying two linear operators 148 7.4. Bilinear form 149 7.5. Quadratic form 150 7.6. Linear operator and basis change 150 7.7. Examples of linear operators 152 7.7.1. Operation f = a ^ F 152 7.7.2. Operation f = a ^ (a ^ F) 152 7.7.3. Operation f = a(b â F) 153 7.7.4. Operation f = a ^ (F ^ a) 155 7.8. Vector rotation Ru, a 156 7.8.1. Expression of the vector rotation 156 7.8.2. Quaternion associated with the vector rotation Ru, a 159 7.8.3. Matrix representation of the vector rotation 160 7.8.4. Basis change and rotation vector 162 Chapter 8. Homogeneity and Dimension 165 8.1. Notion of homogeneity 165 8.2. Dimension 165 8.3. Standard mechanical dimensions 166 8.4. Using dimensional equations 168 Bibliography 171 Index 173.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Aslanov, Vladimir S.
 London : ButterworthHeinemann, 2017.
 Description
 Book — 1 online resource (422 p.)
 Summary

 1. Mathematical Mechanical Preliminaries
 2. Reentry Attitude Dynamics
 3. Dynamics and Control of Coaxial Satellite Gyrostats
 4. Deployment, Dynamics, and Control of a TetherAssisted Return Mission of a Reentry Capsule
 5. Removal of Large Space Debris by a Tether Tow
 6. Original Tasks of Space Mechanics.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Borel, Michel, author.
 London, UK : ISTE, Ltd. ; Hoboken, NJ : Wiley, 2016.
 Description
 Book — 1 online resource.
 Summary

 Introduction ix Table of Notations xv
 Chapter 1. Location of Solid Bodies 1 1.1. The notion of system of reference 1 1.2. Frame of reference 2 1.2.1. Setting up a frame of reference 2 1.2.2. Various types of frames of reference 9 1.3. Location of a solid body 14 1.3.1. The principle of locating a solid 15 1.3.2. Location parameters of a solid 15 1.3.3. Coordinates of the position vector 16 1.3.4. Exercises 20 1.4. Positioning of a system of reference connected to a solid 22 1.4.1. Several examples of location systems of reference 22 1.4.2. General location parameters 26 1.4.3. Euler angles 28 1.4.4. Changes of basis in the Euler representation . 29 1.4.5. Exercises 36 1.5. Vector rotation R u , Î± 44 1.5.1. Exercises 47 1.6. Other exercises 51 1.6.1. Exercise 7  Location of an airplane  Euler angles 51 1.6.2. Exercise 8  Vector rotation 55 1.6.3. Exercise 9  Vector rotation 57 1.6.4. Exercise 10 Vector rotation 59
 Chapter 2. Solid Kinematics 63 2.1. Generalities on moving solids 63 2.1.1. Concept of a rigid material system 63 2.1.2. Notion of time 64 2.1.3. Kinematic components of a solid 65 2.2. Kinematics of a material point 66 2.2.1. Position vector 66 2.2.2. Trajectory of a material point in a reference frame 66 2.2.3. Velocity of a material point in a reference frame 67 2.2.4. Components of the velocity vector or velocity 68 2.2.5. Derivative of a vector in a basis 71 2.2.6. Acceleration vector of a material point in a reference frame 74 2.2.7. Exercises 79 2.3. Velocity field associated with the motion of the rigid solid 85 2.3.1. Fundamental formula for the velocity 85 2.3.2. Use of matrix notation 87 2.3.3. Velocitydistributing torsor 89 2.3.4. Partial distributing 89 2.4. Acceleration field of the rigid solid 91 2.4.1. Derivative in relation to the time of the rate of rotation 91 2.4.2. Derivation of a vector of the solid 92 2.4.3. Fundamental formula of acceleration 92 2.4.4. Matrix notation of the vectorial product 92 2.4.5. Exercises 93 2.5. Motion with fixed plane 102 2.5.1. Position of the problem 102 2.5.2. Instantaneous rotation center 104 2.5.3. Fixed and mobile centroids of the motion 106 2.5.4. The instantaneous center of rotation on the fixed centroid and on the movable centroid 107 2.5.5. Physical interpretation of the notions of fixed centroid and mobile centroid 108 2.5.6. Exercises 109 2.6. Combining motions within a mobile frame of reference 117 2.6.1. Position of the problem 117 2.6.2. Trajectory of a material point in the different frames 118 2.6.3. Combination of velocities 118 2.6.4. Combination of accelerations 123 2.6.5. Application exercises 128 2.7. Relative motion of two rigid solids in contact 141 2.7.1. Position of the problem 141 2.7.2. Velocitydistributing torsors 141 2.7.3. Characterization of motions 142 2.7.4. Nature of the contact between (S1) and (S2) 143 2.7.5. Exercises 145 2.8. Other exercises 156 2.8.1. Exercise 21  Motion with fixed plane 156 2.8.2. Exercise 22  Combination of motions 160 2.8.3. Exercise 23  Kinematics of contact in a system 169
 Chapter 3. Kinetics of Solid Bodies 177 3.1. The mass of a continuous mechanical set (D ) 177 3.1.1. The notion of measure on a continuous mechanical set 178 3.1.2. The volume and the mass of a continuous mechanical set 178 3.2. Center of the measure of Î¼ on (D ) 179 3.2.1. Definition 179 3.2.2. Uniqueness of the center of measure 179 3.2.3. Center of measure of two disjoint sets 180 3.2.4. Coordinates of the center of measure in a system of reference ?'Î»?A 181 3.3. Interpretation of the notion of center of measure 183 3.4. Kinetic torsor of a mechanical set (D ) 183 3.4.1. Definition  linear momentum 183 3.4.2. Kinetic torsor { } S pÎ» of a rigid solid body 185 3.4.3. Inertia operator OS (
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Plumpton, C. (Charles), author.
 Second (SI) edition.  Oxford : Pergamon Press [1971]
 Description
 Book — 1 online resource : illustrations.
 International Congress of Theoretical and Applied Mechanics (18th : 1992 : Haifa, Israel)
 Amsterdam ; New York : Elsevier, 1993.
 Description
 Book — 1 online resource (xxxii, 459 p.) : ill.
 Summary

 Sponsoring organizations and companies
 congress committees
 list of participants
 report on the congress. Opening and closing lectures: instability and turbulence in shear flows, A. Roshko
 micromechanics of fracture, G.I. Barenblatt. Introductory lectures of minisymposia. Instabilities in solid and structural mechanics: material instabilities and phase transitions in thermoelasticity, R. Abeyaratne
 propagating instabilities in structures, S. Kyriakides
 computational approaches to plastic instability in solid mechanics, Y. Tomita. Sea surface mechanics and airsea interaction: the role of wave breaking in airsea interaction, W.K. Melville
 extreme waves and breaking wavelets, O.M. Phillips
 effect of wind and water shear on wave instabilities, P.G. Saffman. Biomechanics: nature's structural engineering of bone on a daily basis, S.C. Cowin
 liquid layer dynamics in pulmonary airways, R.D. Kamm
 energysaving mechanisms in animal movement, R. McN. Alexander. Sectional lectures: controlling chaotic convection, H.H. Bau
 application of structural mechanics to biological systems, C.R. Calladine
 viscous fingering as a pattern forming system, Y. Couder
 mechanics in sport, G. Grimvall
 aerodynamic sound associated with vortex motions  observation and computation, T. Kambe
 nonlinear membrane theory, A. Libai
 on the role of wave propagation and wave breaking in atmosphereocean dynamics, M.E. McIntyre
 computational aspects of integration along the path of loading in elasticplastic problems, J.B. Martin
 constitutive modelling and analysis of creep, damage and creep crack growth under neutron irradiation, S. Murakami
 stability and bifurcation in dissipative media, Q.S. Nguyen
 bubble mechanics  luminescence, noise, and twophase flow, A. Prosperetti
 wave propagation in nonisotropic structures, M.B. Sayir
 selfsimilar multiplier distributions and multiplicative models for energy dissipation in highReynoldsnumber turbulence, K.R. Sreenivasan, G. Stolovitzky
 cardiovascular fluid mechanics, A.A. van Steenhoven et al
 trends in transonic research, J. Zierep. Contributed papers: list of contributed papers presented at the congress.
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(source: Nielsen Book Data)
 Butikov, E. I. (Evgeniĭ Ivanovich), author.
 Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2014]
 Description
 Book — 1 online resource (various pagings) : illustrations.
 Summary

 Preface
 1 Introduction: Getting Started I Review of the Simulations 2 Kepler's Laws
 3 Hodograph of the Velocity Vector
 4 Satellites and Missiles
 5 Active Maneuvers in Space Orbits
 6 Precession of an Equatorial Orbit
 7 Binary Star  the TwoBody Problem 8 ThreeBody Systems 9 ManyBody Systems in Celestial Mechanics II The Simulated Phenomena
 10 Phenomena and Concepts
 11 Theoretical Background Glossary.
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(source: Nielsen Book Data)
19. Teaching energy across the sciences, K12 [2016]
 Arlington, Virginia : NSTA Press/National Science Teachers Association, [2016]
 Description
 Book — 1 online resource
 Summary

 Section 1. Exploring energy as a crosscutting concept
 section 2. Teaching energy across the life, physical, and earth sciences
 section 3. Supporting teachers in emphasizing energy as a crosscutting concept.
(source: Nielsen Book Data)
 Balthazar, José Manoel.
 Zurich : Trans Tech Publications, 2016.
 Description
 Book — 1 online resource (127 pages). Digital: data file.
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