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Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians (Hardback)

Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians (Hardback)

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VERY GOOD: The cover and pages are in excellent condition. The cover is free of marks and blemishes. The binding is still tight. There is no yellowing on the pages.

Product Details

Covering subjects ranging from an Introduction to Analytical Mechanics to Hamiltonian/Canonical Methods: Equations of Hamilton and Routh; Canonical Formalism this book is both a desk reference and text book covering Analytical Mechanics from the point of view of Engineers, Physicists and Mathematicians.

Table of Contents

Introduction

  • 1 Introduction to Analytical Mechanics
  • 2 History of Theoretical Mechanics: A Bird's Eye View
  • 3 Suggestions to the Reader
  • 4 Abbreviations, Symbols, Notations, Formulae

CHAPTER 1 BACKGROUND: BASIC CONCEPTS AND EQUATIONS OF PARTICLE AND RIGID-BODY MECHANICS

  • 1.1 Vector and (Cartesian) Tensor Algebra
  • 1.2 Space-Time Axioms: Particle Kinematrics
  • 1.3 Bodies and their Masses
  • 1.4 Force; Law of Newton—Euler
  • 1.5 Space-Time and the Principle of Galilean Relativity
  • 1.6 The Fundamental Principles (or Balance Laws) of General System Mechanics
  • 1.7 Accelerated (Noninertial) Frames of Reference (or Relative Motion, or Moving Axes); Angular Velocity and Acceleration
  • 1.8 The Rigid Body: Introduction
  • 1.9 The Rigid Body: Geometry of Motions and Kinematics (Summary of Basic Theorems)
  • 1.10 The Rigid Body: Geometry of Rotational Motion; Finite Rotation
  • 1.11 The Rigid Body: Active and Passive Interpretations of a Proper Orthogonal Tensor; Successive Finite Rotations
  • 1.12 The Rigid Body: Eulerian Angles
  • 1.13 The Rigid Body: Transformation Matrices (Direction Cosines) Between Space-Fixed and Body-Fixed Triads; and Angular Velocity Components along Body-Fixed Axes, for All-Sequences of Eulerian Angles
  • 1.14 The Rigid Body: An Introduction to Quasi Coordinates
  • 1.15 The Rigid Body: Tensor of Inertia, Kinetic Energy
  • 1.16 The Rigid Body: Linear and Angular Momentum
  • 1.17 The Rigid Body: Kinetic Energy and Kinetics of Translation and Rotation (Eulerian "Gyro Equations")
  • 1.18 The Rigid Body: Contact Forces, Friction

CHAPTER 2 KINEMATICS OF CONSTRAINED SYSTEMS (i.e., LAGRANGEAN KINEMATICS)

  • 2.1 Introduction
  • 2.2 Introduction to Constraints and their Classifications
  • 2.3 Quantitative Introduction to Nonholonomicity
  • 2.4 System Positional Coordinates and System Forms of the Holonomic Constraints
  • 2.5 Velocity, Acceleration, Admissible and Virtual Displacements; in System Variables
  • 2.6 System Forms of Linear Velocity (Pfaffian) Constraints
  • 2.7 Geometrical Interpretations of Constraints
  • 2.8 Noncommutativity versus Nonholonomicity; Introduction to the Theorem of Frobenius
  • 2.9 Quasi Coordinates, and their Calculus
  • 2.10 Transitivity, or Transpositional, Rotations; Hamel Coefficients
  • 2.11 Pfaffian (Velocity) Constraints via Quasi Variables, and their Geometrical Interpretation
  • 2.12 Constrained Transitivity Equations, and Hamel's Form of Frobenus' Theorem
  • 2.13 General Examples and Problems

CHAPTER 3 KINETICS OF CONSTRAINED SYSTEMS (i.e., LAGRANGEAN KINETICS)

  • 3.1 Introduction
  • 3.2 The Principle of Lagrange
  • 3.3 Virtual Work of Inertial Forces (δI), and Related Kinematico-Inertial Identites
  • 3.4 Virtual Work of Forces (δW), and Constraint Reactions (δWR)
  • 3.5 Equations of Motion via Lagrange's Principle: General Forms
  • 3.6 The Central Equation (The Zentralgleichung of Heun and Hamel)
  • 3.7 The Principle of Relaxation of Constraints (The Lagrange-Hamel Befreiungsprinzip)
  • 3.8 Equations of Motion: Special Forms
  • 3.9 Kinetic and Potential Energies: Energy Rate, or Power, Theorems
  • 3.10 Lagrange's Equations: Explicit Forms; and Linear Variational Equations (or Method of Small Oscillations)
  • 3.11 Appell's Equations: Explicit Forms
  • 3.12 Equations of Motion: Integration and Conservation Theorems
  • 3.13 The Rigid Body: Lagrangean-Eulerian Kinematico-Inertial Identities
  • 3.14 The Rigid Body: Appellian Kinematico-Inertial Identities
  • 3.15 The Rigid Body: Virtual Work of Forces
  • 3.16 Relative Motion (or Moving Axes/Frames via Lagrange's Method)
  • 3.17 Servo (or Control) Constraints
  • 3.18 General Examples and Problems
  • APPENDIX 3.A1 Remarks on the History of the Hamel-type Equations of Analytical Mechanics
  • APPENDIX 3.A2 Critical Comments on Virtual Displacements/Work and Lagrange's Principle

CHAPTER 4 IMPULSIVE MOTION

  • 4.1 Introduction
  • 4.2 Brief Overview of the Newton-Euler Impulsive Theory
  • 4.3 The Lagrangean Impulsive Theory; Namely, Constrained Discontinuous Motion
  • 4.4 The Appellian Classification of Impulsive Constraints, and Corresponding Equations of Impulsive Motion
  • 4.5 Impulsive Motion via Quasi Variables
  • 4.6 Extremum Theorems of Impulsive Motion (of Carnot, Kelvin, Bertrand, Robin, et al.)

CHAPTER 5 NONLINEAR NONHOLONOMIC CONSTRAINTS

  • 5.1 Introduction
  • 5.2 Kinematics: The Nonlinear Transitivity Equations
  • 5.3 Kinetics: Variational Equations/Principles; General and Specific Equations of Motion (Johnson, Hamel, et al.)
  • 5.4 Second- and Higher-Order Constraints

CHAPTER 6 DIFFERENTIAL VARIATIONAL PRINCIPLES, AND ASSOCIATED GENERALIZED EQUATIONS OF MOTION OF NIELSEN, TSENOV, ET AL.

  • 6.1 Introduction
  • 6.2 The General Theory
  • 6.3 Principle of Jourdain, and Equations of Nielsen
  • 6.4 Introduction to the Principle of Gauss and the Equations of Tsenov
  • 6.5 Additional Forms of the Equations of Nielsen and Tsenov
  • 6.6 The Principle of Gauss (Extensive Treatment)
  • 6.7 The Principle of Hertz

CHAPTER 7 TIME-INTEGRAL THEOREMS AND VARIATIONAL PRINCIPLES

  • 7.1 Introduction

TIME-INTEGRAL THEOREMS

  • 7.2 Time-Integral Theorems: Pfaffian Constraints, Holonomic Variables
  • 7.3 Time-Integral Theorems: Pfaffian Constraints, Linear Nonholonomic Variables
  • 7.4 Time-Integral Theorems: Nonlinear Velocity Constraints, Holonomic Variables
  • 7.5 Time-Integral Theorems: Nonlinear Velocity Constraints, Nonlinear Nonholonomic Variables

TIME-INTEGRAL VARIATIONAL PRINCIPLES (IVP)

  • 7.6 Hamilton's Principle versus Calculus of Variations
  • 7.7 Integral Variational Equations of Mechanics
  • 7.8 Special Integral Variational Principles (of Suslov, Voronets, et al.)
  • 7.9 Noncontemporaneous Variations; Additional IVP Forms
  • APPENDIX 7.A Extremal Properties of the Hamiltonian Action (Is the Action Really a Minimum; Namely Least?)

CHAPTER 8 INTRODUCTION TO HAMILTONIAN/CANONICAL METHODS: EQUATIONS OF HAMILTON AND ROUTH; CANONICAL FORMALISM

  • 8.1 Introduction
  • 8.2 The Hamiltonian, or Canonical, Central Equation and Hamilton's Canonical Equation of Motion
  • 8.3 The Routhian Central Equations and Routh's Equations of Motion
  • 8.4 Cyclic Systems; Equations of Kelvin-Tait
  • 8.5 Steady Motion (of Cyclic Systems)
  • 8.6 Stability of Steady Motion (of Cyclic Systems)
  • 8.7 Variations of Constraints (or Parameters)
  • 8.8 Canonical Transformations
  • 8.9 Canonicity Conditions via Poisson's Brackets (PB)
  • 8.10 The Hamilton-Jacobi Theory
  • 8.11 Hamilton's Principal and Characteristic Functions, and Associated Variational Principles/Differential Equations
  • 8.12 Intergal Variants
  • 8.13 Noether's Theorem
  • 8.14 Periodic Motions; Action-Angle Variables
  • 8.15 Adiabatic Invariants
  • 8.16 Canonical Perturbation Theory in Action-Angle Variables

END MATTER

  • References and Suggested Reading
  • Index
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AUTHOR: Papastravridis;John G. Ph.D
PUBLISHER: Oxford University Press
ISBN-13: 9780195126976
ISBN-10: 0195126971
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Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians (Hardback)
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