Analytical Mechanics : A Comprehensive Treatise on the Dynamics of Constrained Systems (Reprint Edition)
John G. Papastavridis
Bok Engelsk 2014 · Electronic books.
| Annen tittel | |
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| Utgitt | Singapore : : World Scientific Publishing Company, , 2014.
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| Omfang | 1 online resource (1417 p.)
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| Utgave | Reprint ed.
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| Opplysninger | Description based upon print version of record.. - PREFACE TO THE CORRECTED REPRINT; PREFACE; ACKNOWLEDGMENTS; Contents; Words of Wisdom and Beauty; 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; 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 Kinematics; 1.3 Bodies and their Masses; 1.4 Force; Law of Newton-Euler; 1.5 Space-Time and the Principle of Galilean Relativity. - 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; 2 KINEMATICS OF CONSTRAINED SYSTEMS (i.e., LAGRANGEAN KINEMATICS). - 1.6 The Fundamental Principles (or Balance Laws) of General System Mechanics1.7 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 Motion 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. - 2.1 Introduction2.2 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 Interpretation 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, Relations. - 3.6 The Central Equation (The Zentralgleichung of Heun and Hamel). - Hamel Coefficients2.11 Pfaffian (Velocity) Constraints via Quasi Variables, and their Geometrical Interpretation; 2.12 Constrained Transitivity Equations, and Hamel's Form of Frobenius' Theorem; 2.13 General Examples and Problems; 3 KINETICS OF CONSTRAINED SYSTEMS (i.e., LAGRANGEAN KINETICS; 3.1 Introduction; 3.2 The Principle of Lagrange (LP); 3.3 Virtual Work of Inertial Forces ( I), and Related Kinematico-Inertial Identities; 3.4 Virtual Work of Forces: Impressed ( 'W) and Constraint Reactions ( 'WR); 3.5 Equations of Motion via Lagrange's Principle: General Forms. - This is a comprehensive, state-of-the-art, treatise on the energetic mechanics of Lagrange and Hamilton, that is, classical analytical dynamics, and its principal applications to constrained systems (contact, rolling, and servoconstraints). It is a book on advanced dynamics from a unified viewpoint, namely, the kinetic principle of virtual work, or principle of Lagrange. As such, it continues, renovates, and expands the grand tradition laid by such mechanics masters as Appell, Maggi, Whittaker, Heun, Hamel, Chetaev, Synge, Pars, Luré, Gantmacher, Neimark, and Fufaev. Many completely solved exa
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 9789814338714
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