Elements of Newtonian Mechanics
Including Nonlinear Dynamics
(Sprache: Englisch)
In the second edition, a number of misprints that appeared in the first edition have been corrected. In addition to this, we have made improvements based on the experience gathered in the use of the first English edition of the book in the introductory...
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In the second edition, a number of misprints that appeared in the first edition have been corrected. In addition to this, we have made improvements based on the experience gathered in the use of the first English edition of the book in the introductory course in physics at the University of Copenhagen. A chapter introducing nonlinear dynamics has been added. The purpose of this chapter is to provide supplementary reading for the students who are interested in this area of active research, where Newtonian mechanics plays an essential role. The students who wish to dig deeper, should consult texts dedicated to the study of nonlinear dynamical systems and chaos. The literature list at the end of this book contains several references for the topic. The book still contains a one-semester (15 weeks) first university course on Newtonian mechanics. This necessarily introduces some constraints on the choice of topics and the level of mathematical sophistication expected from the reader. If one looks for discussions of technical issues, such as the physics behind various manifestations of friction, or the tensorial nature of the rotation vector, one will look in vain. The book contains what we feel are the essential aspects of Newtonian Mechanics. It is a pleasure again to thank Springer-Verlag and in particular Dr. H. J. KOisch and the staff at the Heidelberg office for helpfulness and professional collaboration.
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 for the best teaching at the University of Copenhagen, Denmark. More than 100 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 fundamental 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.
Inhaltsverzeichnis zu „Elements of Newtonian Mechanics “
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: 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.- 8.6 The Gravitational Field Around a Homogeneous Sphere.- 8.7 Examples.- 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.- 9.4 Review: Center of Mass andCenter-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
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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.- 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: Linear Motion and Rotation About a Fixed Axis.- 11.11 Problems.- 12. The Laws of Motion.- 12.1 Review: Classical Mechanics.- 12.2 Remarks on the Three Conservation Theorems.- 12.3 Examples.- 12.4 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.- 16. Remarks on Nonlinearity and Chaos.- 16.1 Determinism vs Predictability.- 16.2 Linear and Nonlinear Differential Equations.- 16.3 Phase Space.- 16.4 A Forced, Damped Nonlinear Oscillator.- 16.5 Liapunov Exponents.- 16.6 Chaos in the Solar System.- 16.7 Problems.- Appendix. Vectors and Vector Calculus.- Selected References.- Answers to Problems.
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Bibliographische Angaben
- Autoren: Jens M. Knudsen , Poul G. Hjorth
- 1996, 2. Aufl., XVII, 437 Seiten, Maße: 15,5 x 23,6 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3540608419
- ISBN-13: 9783540608417
Sprache:
Englisch
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