Classical Mechanics : Theory and Mathematical Modeling
Emmanuele. DiBenedetto
Bok Engelsk 2011 · Electronic books.
| Annen tittel | |
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| Utgitt | New York : Birkhäuser , cop. 2011
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| Omfang | 1 online resource (363 p.)
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| Opplysninger | Description based upon print version of record.. - Classical Mechanics; Contents; Preface; 1 GEOMETRY OF MOTION; 1 Trajectories in R3 and Intrinsic Triads; 2 Areolar Velocity and Central Motions; 3 Geometry of Rigid Motions; 4 The Euler Angles; 5 Rotation Matrices and Angular Velocity; 6 Velocity and Acceleration; 6.1 Translations; 6.2 Precessions; 6.3 Rototranslations; 7 The Axis of Motion; 8 Relative Rigid Motions and Coriolis's Theorem; 9 Composing Rigid Motions; 9.1 Connecting the Euler Angles and; 10 Fixed and Moving Axodes; 10.1 Precessions: Fixed and Moving Cones; 11 Plane Rigid Motions; 11.1 Center of Instantaneous Rotation. - 1.1c Elliptic Coordinates1.2c Parabolic Coordinates; 1.3c Spherical Coordinates; 1.4c Cylindrical Coordinates; 2c Constrained Mechanical Systems; 2.1c Holonomic and Nonholonomic Constraints; 2.2c Disk Rolling without Slipping on a Line; 2.3c Sphere Rolling without Slipping in a Plane; 2.4c Rigid Rod with Constrained Extremities; 3c Intrinsic Metrics and First Fundamental Form; 3.1c A Parameterization of the Torus; 4c Geodesics; 5c Examples of Geodesics; 5.1c The Clairaut Theorem; 3 DYNAMICS OF A POINT MASS; 1 Newton's Laws and Inertial Systems; 2 Mathematical Formulations of (1.1)-(1.2). - 11.1c Parametric Equations of Fixed and Moving Centrodes11.2c Centrodes for Hypocycloidal Motions; 11.3c The Cardano Device; 11.4c More on the Cardano Device; 2 CONSTRAINTS AND LAGRANGIAN COORDINATES; 1 Constrained Trajectories; 2 Constrained Mechanical Systems; 2.1 Actual and Virtual Displacements; 2.2 Holonomic Constraints; 2.3 Unilateral Constraints; 3 Intrinsic Metrics and First Fundamental Form; 4 Geodesics; 5 Examples of Geodesics; 5.1 Geodesics in a Plane; 5.2 Geodesics on a Sphere; 5.3 Geodesics on Surfaces of Revolution; Problems and Complements; 1c Constrained Trajectories. - 11.2 CentrodesProblems and Complements; 2c Areolar Velocity and Central Motions; 2.1c Cycloidal Trajectories; 2.2c The Brachistochrone and Tautochrone; 2.3c Hypocycloidal and Epicycloidal Trajectories; 2.4c Kepler's Gravitational Laws; 2.5c Apsidal Points; 2.6c Elliptic Trajectories of Some Central Motions; 8c Relative Rigid Motions and Coriolis's Theorem; 9c Composing Rigid Motions; 9.1c Connecting the Euler Angles and; 10c Fixed and Moving Axodes; 10.1c Cone with Fixed Vertex and Rolling without Slipping; 10.2c Cylinder Rolling without Slipping; 11c Plane Rigid Motions. - 3 General Theorems of Point-Mass Dynamics3.1 Positional and Central Forces; 3.2 Conservative Forces; 4 The Two-Body Problem; 4.1 Gravitational Trajectories; 5 Newton's and Kepler's Laws and Inertial Systems; 6 Dynamics of a Point Mass Subject to Gravity; 6.1 On the Notion of Weight, Vertical Axis, and Gravity; 6.2 Gravitational Motion near the Surface of Earth; 7 Motion of a Constrained Point Mass; 7.1 Smooth Constraints and Relative Energy; 7.2 Rough Constraints and Relative Energy; 7.3 Remarks on Fixed Constraints; 7.4 Remarks on the Case of F Conservative; 8 The Mathematical Pendulum. - Problems and Complements. - * Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a ""unifying"" language, but also to exemplify its role as a catalyst behind new concepts and discoveries
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 9780817645267
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