Classical Dynamics : A Contemporary Approach
Jorge V. José
Bok Engelsk 1998 · Electronic books.
| Utgitt | Cambridge : Cambridge University Press , 1998
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| Omfang | 1 online resource (697 p.)
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| Opplysninger | Description based upon print version of record.. - Cover; Half Title; Title Page; Copyright; Dedication; Contents; List of Worked Examples; 2.1.1 Constraints; Preface; Two Paths Through the Book; 1 Fundamentals of Mechanics; 1.1 Elementary Kinematics; 1.1.1 Trajectories of Point Particles; 1.1.2 Position, Velocity, and Acceleration; 1.2 Principles of Dynamics; 1.2.1 Newton's Laws; 1.2.2 The Two Principles; Principle 1; Principle 2; Discussion; 1.2.3 Consequences of Newton's Equations; Introduction; Force is a Vector; 1.3 One-Particle Dynamical Variables; 1.3.1 Momentum; 1.3.2 Angular Momentum; 1.3.3 Energy and Work; In Three Dimensions. - 2.1.3 Examples of Configuration ManifoldsThe Finite Line; The Circle; The Plane; The Two-Sphere S[sup(2)]; The Double Pendulum; Discussion; 2.2 Lagrange's Equations; 2.2.1 Derivation of Lagrange's Equations; 2.2.2 Transformations of Lagrangians; Equivalent Lagrangians; Coordinate Independence; Hessian Condition; 2.2.3 Conservation of Energy; 2.2.4 Charged Particle in an Electromagnetic Field; The Lagrangian; A Time-Dependent Coordinate Transformation; 2.3 Central Force Motion; 2.3.1 The General Central Force Problem; Statement of the Problem; Reduced Mass; Reduction to Two Freedoms. - 3.2 Symmetry and Conservation3.2.1 Cyclic Coordinates; Invariant Submanifolds and Conservation of Momentum; Transformations, Passive and Active; Three Examples; 3.2.2 Noether's Theorem; Point Transformations; The Theorem; 3.3 Nonpotential Forces; 3.3.1 Dissipative Forces in the Lagrangian Formalism; Rewriting the EL Equations; The Dissipative and Rayleigh Functions; 3.3.2 The Damped Harmonic Oscillator; 3.3.3 Comment on Time-Dependent Forces; 3.4 A Digression on Geometry; 3.4.1 Some Geometry; Vector Fields; One-Forms; The Lie Derivative; 3.4.2 The Euler-Lagrange Equations. - 3.4.3 Noether's Theorem. - Application to One-Dimensional Motion1.4 Many-Particle Systems; 1.4.1 Momentum and Center of Mass; Center of Mass; Momentum; Variable Mass; 1.4.2 Energy; 1.4.3 Angular Momentum; 1.5 Examples; 1.5.1 Velocity Phase Space and Phase Portraits; The Cosine Potential; The Kepler Problem; 1.5.2 A System with Energy Loss; 1.5.3 Noninertial Frames and the Equivalence Principle; Equivalence Principle; Rotating Frames; Problems; 2 Lagrangian Formulation of Mechanics; 2.1 Constraints and Configuration Manifolds; Constraint Equations; Constraints and Work; 2.1.2 Generalized Coordinates. - The Equivalent One-Dimensional Problem2.3.2 The Kepler Problem; 2.3.3 Bertrand's Theorem; 2.4 The Tangent Bundle TQ; 2.4.1 Dynamics on TQ; Velocities Do Not Lie in Q; Tangent Spaces and the Tangent Bundle; Lagrange's Equations and Trajectories on TQ; 2.4.2 TQ as a Differential Manifold; Differential Manifolds; Tangent Spaces and Tangent Bundles; Application to Lagrange's Equations; Problems; 3 Topics in Lagrangian Dynamics; 3.1 The Variational Principle and Lagrange's Equations; 3.1.1 Derivation; The Action; Hamilton's Principle; Discussion; 3.1.2 Inclusion of Constraints. - A comprehensive and completely up to date graduate-level textbook on classical dynamics with many worked examples and over 200 homework exercises.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 0521631769. - 0521636361
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