Knudsen / Hjorth Elements of Newtonian Mechanics

Erscheinungsjahr 2012
ISBN: 978-3-642-97599-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 413 Seiten, Web PDF

This book is intended as a textbook for an entry-level university course in Newtonian mechanics for students of physics, astronomy, and the engineering sciences. The material has been used as a first-semester text for first-year undergraduates at the Niels Bohr Institute, which is part of the University of Copenhagen. Our way of presenting Newtonian mechanics is influenced by the writings of the late Max Born. Also, the Feynman Lectures on Physics have been an important source of inspiration. In fact, the idea for the book came when we read Section 16.1 of Volume 1 of the Feynman Lectures. Ideas from the well-known Berkeley Physics Course may also be traced in the text. All of the books quoted in the literature list have, in one way or another, served as a source for our lectures for undergraduates. It is assumed that the students already have a rudimentary knowledge of Newtonian mechanics, say at the high-school level. Some background in vectors and elementary calculus is also required, i.e., the students should know how to add vectors as well as how to differentiate and integrate elementary functions. The Appendix contains the required background for the use of vectors in Newtonian mechanics.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Knudsen, Jens M.

Hjorth, Poul G.

Inhaltsverzeichnis

1. The Foundation of Classical Mechanics.- 1.1 Principia.- 1.2 Prerequisites for Newton.- 1.3 The Masterpiece.- 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.- 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.- 3.5 Problem.- 4. The Galilei Transformation.- 4.1 The Galilei Transformation.- 4.2 Galileo Speaks.- 4.3 Problems.- 5. The Motion of the Earth.- 5.1 Examples.- 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.- 6.4 The Centrifugal Force.- 6.5 Tidal Fields.- 6.6 The Coriolis Force.- 6.7 Tidal Forces and Local Inertial Frames.- 6.8 The Foucault Pendulum.- 6.9 Newton’s Bucket.- 6.10 Review of Chapter 6.- 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.- 8.6 The Gravitational Field Around a Homogeneous Sphere.- 8.7 Examples.- 8.8 Review: Conservation 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.- 9.4 Review.- 9.5 Problems.- 10. The AngularMomentum 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.- 10.8 Examples of Conservation of Angular Momentum.- 11. Rotation of a Rigid Body.- 11.1 Equations of Motion.- 11.2 The Rotation Vector.- 11.3 Kinetic Energy.- 11.4 An Arbitrary Rigid Body in Rotation Around a Fixed Axis.- 11.5 Calculation of the Moment of Inertia for Simple Bodies.- 11.6 Equation of Motion for a Rigid Body Rotating Around a Fixed Axis.- 11.7 Work and Power in the Rotation of a Rigid Body Around a Fixed Axis.- 11.8 The Angular Momentum Theorem Referred to Various Points.- 11.9 Examples.- 11.10 Review: Comparison Between Linear Motion and Rotation About a Fixed Axis.- 11.11 Problems.- 12. The Laws of Motion.- 12.1 Classical Mechanics: A Review.- 12.2 Examples.- 12.3 Problems.- 13. The General Motion of a Rigid Body.- 13.1 Inertia in Rotational Motion.- 13.2 The Inertia Tensor.- 13.3 Euler’s Equations.- 13.4 Kinetic Energy.- 13.5 Determination of the Principal Coordinate System.- 13.6 Problems.- 14. The Motion of the Planets.- 14.1 Tycho Brahe.- 14.2 Kepler and the Orbit of Mars.- 14.3 Conic Sections.- 14.4 Newton’s Law of Gravity Derived from Kepler’s Laws.- 14.5 The Kepler Problem.- 14.6 The Effective Potential.- 14.7 The Two-Body Problem.- 14.8 Double Stars: The Motion of the Heliocentric Reference Frame.- 14.9 Review: Kepler Motion.- 14.10 Examples.- 14.11 Problems.- 15. Harmonic Oscillators.- 15.1 Small Oscillations.- 15.2 Energy in Harmonic Oscillators.- 15.3 Free Damped Oscillations.- 15.4 Energy in Free, Weakly Damped Oscillations.-15.5 Forced Oscillations.- 15.6 The Forced Damped Harmonic Oscillator.- 15.7 Frequency Characteristics.- 15.8 Power Absorption.- 15.9 The Q- Value of a Weakly Damped Harmonic Oscillator.- 15.10 The Lorentz Curve.- 15.11 Complex Numbers.- 15.12 Problems.- Appendix. Vectors and Vector Calculus.- Selected References.- Answers to Problems.