Elements of Newtonian mechanics : including nonlinear dynamics : with 324 figures, 109 problems with solutions, and 92 worked examples

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. 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 (Arets Harald, 1990; named after the late mathematician Harald Bohr). 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 will give the student a solid introduction to an important area of physics. 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. Front Matter....Pages N2-XVII The Foundation of Classical Mechanics....Pages 1-26 Newton’s Five Laws....Pages 27-72 Gravitational and Inertial Mass....Pages 73-81 The Galilei Transformation....Pages 83-93 The Motion of the Earth....Pages 95-100 Motion in Accelerated Reference Frames....Pages 101-151 The Problem of Motion....Pages 153-165 Energy....Pages 167-192 The Center-of-Mass Theorem....Pages 193-217 The Angular Momentum Theorem....Pages 219-234 Rotation of a Rigid Body....Pages 237-271 The Laws of Motion....Pages 273-300 The General Motion of a Rigid Body....Pages 301-332 The Motion of the Planets....Pages 333-371 Harmonic Oscillators....Pages 373-393 Remarks on Nonlinearity and Chaos....Pages 395-416 Back Matter....Pages 417-439 It was an important event in the history of physics when Sir Isaac Newton in 1687 published his book Philosophiae Naturalis Principia Mathematica.