Elements of Newtonian Mechanics: Including Nonlinear Dynamics - Softcover

Knudsen, Jens M.; Hjorth, Poul G.

Softcover

ISBN 10: 3540608419 ISBN 13: 9783540608417

Verlag: Springer, 1996

Inhaltsangabe

1. The Foundation of Classical Mechanics.- 1.1 Principia.- 1.2 Prerequisites for Newton.- 1.3 The Masterpiece.- The Acceleration of Gravity.- Circular Motion.- Communication Satellite.- Horizontal Throw.- The Gravitational Constant.- String Force.- Forces and Tension.- Dimensional Analysis.- 1.4 Concluding Remarks.- 1.5 Problems.- 2. Newton's Five Laws.- 2.1 Newton's Laws of Motion.- 2.2 Integration of the Equation of Motion.- Constant Force.- The Harmonic Oscillator.- Mass on a Spring in the Gravitational Field of Earth.- Sphere Falling Through a Liquid.- Solid Against Solid.- The Atwood Machine.- Force in Harmonic Motion.- Charged Particle in a Uniform Magnetic Field.- Thomson's Experiment.- Work and Energy in Linear Motion of a Particle.- Free Fall Towards the Sun from a Great Distance.- Momentum Conservation.- Inelastic Collisions.- Rocket Propulsion.- Some Qualitative Remarks on Rocket Propulsion.- Ball Against a Wall.- 2.3 Problems.- 3. Gravitational and Inertial Mass.- 3.1 Gravitational Mass.- 3.2 Inertial Mass.- 3.3 Proportionality Between Inertial and Gravitational Mass.- 3.4 Newton's Experiment.- The Satellite.- An Elevator in Free Fall.- Three Balls.- 3.5 Problem.- 4. The Galilei Transformation.- 4.1 The Galilei Transformation.- 4.2 Galileo Speaks.- Velocity Transformation.- 4.3 Problems.- 5. The Motion of the Earth.- 5.1 Examples.- Vectors and the Rotation of a Rigid Body.- Angular Velocities in the Solar System.- 5.2 Problems.- 6. Motion in Accelerated Reference Frames.- 6.1 Newton's 2nd Law Within Accelerated Reference Frames.- 6.2 The Equivalence Principle of Mechanics.- 6.3 The Einstein Box.- Balloon in Accelerated Frame.- Mass on an Oscillating Plate.- Pendulum in an Elevator.- 6.4 The Centrifugal Force.- Earth's Orbit Around the Sun.- Grass on a Rotating Disk.- The Variation of g with Latitude.- 6.5 Tidal Fields.- The Roche Limit.- 6.6 The Coriolis Force.- Coriolis Force on a Train.- Particle on a Frictionless Disc.- The Vertical Throw.- 6.7 Tidal Forces and Local Inertial Frames.- Global and Local Inertial Frames.- 6.8 The Foucault Pendulum.- 6.9 Newton's Bucket.- 6.10 Review: Fictitious Forces.- 6.11 Problems.- 7. The Problem of Motion.- 7.1 Kinematic and Dynamic Views of the Problem of Motion.- 7.2 Einstein Speaks.- 7.3 Symmetry.- 7.4 The Symmetry (Invariance) of Newton's 2nd Law.- 7.5 Limited Absolute Space.- 7.6 The Asymmetry (Variance) of Newton's 2nd Law.- 7.7 Critique of the Newtonian View.- 7.8 Concluding Remarks.- 8. Energy.- 8.1 Work and Kinetic Energy.- 8.2 Conservative Force Fields.- 8.3 Central Force Fields.- 8.4 Potential Energy and Conservation of Energy.- 8.5 Calculation of Potential Energy.- Constant Gravitational Field.- Spring Force.- Gravity Outside a Homogeneous Sphere.- 8.6 The Gravitational Field Around a Homogeneous Sphere.- 8.6.1 The Field Around a Spherical Shell.- 8.6.2 A Solid Sphere.- 8.7 Examples.- Particle on a Frictionless Curve.- String Force in the Pendulum.- The Gravitational Potential Outside the Earth.- Potential Energy Due to Electric Forces.- A Tunnel Through the Earth.- The Asymmetry of Nature.- 8.8 Review: Conservative Forces and Potential Energy.- 8.9 Problems.- 9. The Center-of-Mass Theorem.- 9.1 The Center of Mass.- 9.2 The Center-of-Mass Frame.- 9.3 Examples.- Two Masses Connected with a Spring.- Inelastic Collisions.- The Collision Approximation.- Freely Falling Spring.- The Wedge.- 9.4 Review: Center of Mass and Center-of-Mass Theorems.- 9.5 Comments on the Conservation Theorems.- 9.6 Problems.- 10. The Angular Momentum Theorem.- 10.1 The Angular Momentum Theorem for a Particle.- 10.2 Conservation of Angular Momentum.- 10.3 Torque and Angular Momentum Around an Axis.- 10.4 The Angular Momentum Theorem for a System of Particles.- 10.5 Center of Gravity.- 10.6 Angular Momentum Around the Center of Mass.- 10.7 Review: Equations of Motion for a System of Particles.- 10.8 Examples of Conservation of Angular Momentum.- Particle in Circular Motion.- Rotation o

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This textbook provides a thorough introduction to Newtonian Mechanics and is intended for university students in physics, astronomy and engineering. It is based on a course for which Dr Knudsen earned an award as the best introductory course at the university of Copenhagen, Denmark. About 190 problems with solutions and 84 worked examples help the student to grasp the essential aspects of the subject, and to develop proficiency in using the powerful methods of Newtonian mechanics. Moreover, the problem of motion and the concept of inertial frames is faced from the very beginning, and runs through the entire development of classical mechanics. This new and fresh approach is presented in its second edition, which has been revised and enlarged by a new chapter on nonlinear dynamics.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1996
• Sprache: Englisch
• ISBN 10: 3540608419
• ISBN 13: 9783540608417
• Einband: Tapa blanda
• Auflage: 2
• Anzahl der Seiten: 460
• Kontakt zum Hersteller: Nicht verfügbar