My Reasons for Writing This Mechanics Textbook
Over a period of more than 40 years, I taught Physics at the university level. During this time I taught every non-laboratory course in the standard curriculum, as well as elective courses at both the undergraduate and undergraduate levels. In addition, for the period 1993-2006 I was a co-director of the Science and Mathematics Initiative for Learning Enhancement (SMILE) program at IIT. The objectives of that program were to encourage experience-based teaching of basic science in the elementary grades, as well as to form an informal "support group" for secondary level teachers of science and mathematics. In my opinion, these secondary level science teachers are very dedicated to the teaching of science. Furthermore, they have an innate curiosity concerning the structure of modern science. While many of them lack the background in calculus and higher mathematics to grasp the quantitative aspects of modern physics, they certainly have a very strong interest in the subject. As a theoretical physicist by education and research interests, I found it interesting and challenging to explain some aspects of modern science. In addition, I learned a great deal from them on "practical" questions, as well as on pedagogy and presentation of ideas.
I have have taught both the undergraduate and graduate courses in mechanics several times over the years. Each time I was disappointed my the choice of textbook. My classroom lectures were based upon the internationally renowned Course in Theoretical Physics, Volume 5: Mechanics by Landau and Lifshitz. I admire this book for its concise statements of the principles of mechanics, as well as its compact format. In my opinion, the large, heavy textbooks have created substantial interference to the educational process. These texts are too massive and bulky for students to carry with them to classes, as well as to study between classes. In practical terms, their sheer size essentially guarantees that physics will be the topic studied latest in the evening by a typical student. I do not approve of massive textual material, since it leads to a "physics last" approach to the subject.
As much as I have admired the Mechanics book by Landau and Lifshitz, I never used it as a textbook, because it does not mesh well into the standard curriculum. Namely it does not contain a sufficient number of exercises for students to work out -- and continual attention to homework exercises is an integral component of the study of mechanics. In addition, it is hopelessly out of date as far as numerical exercises and modern developments are concerned. In this text I have included over 20 programs in the high level programming language Mathematica™, as well as graphical display of typical output in this programming language. Students may use these programs to vary input and observe the corresponding changes in output in a variety of mechanical systems.
A teacher typically explains the principles of mechanics and discusses the solutions to homework exercises. The requirement of daily drill by students is essential, but in recent years the educational system has changed continually and dramatically because of the Internet, because it is simple enough to find worked-out solutions to homework problems for almost any textbook that has ever been published. The educational hierarchy has been slow to respond to this "short-circuit" of the educational process. Traditionally, it has adopted the "Pollyanna'' approach of expecting - dreaming - hoping - imagining - presuming that students will not copy solutions, when the information is available after a few "mouse-clicks". In my opinion, we should recognize that collaboration, assistance, internet searches, and library research are legitimate activities for working through homework exercises, and they should be encouraged to promote mastery of the material. My approach in teaching was to grant a small amount of credit (say, 15% of the total grade) to those who develop careful solutions, and who explain their approach in detail. A substantial amount of credit should be allocated to "higher level" projects, in which a particular subject is analyzed and explained in detail, using numerical tools to analyze questions that arise.
How do we discourage the distribution and development of "solution manuals" to standard textbooks? In my book I have provided extensive information on how to solve virtually all of the exercises at the end of the chapter, so that students will have the same information -- a level playing field in the course. Of course, students can still "mindlessly" copy solutions from various sources -- but at the risk of failing to meet the principal objective of such exercises; namely, to learn how to solve mechanics problems by applying the basic principles.
I do not feel that other texts make students sufficiently aware of the multicultural and multilingual aspects in the development of classical mechanics. To address this need, I have included historical remarks from a number of the founders of mechanics --- in the original language (with apologies to typos that may have arisen along the way). Although English is almost the universal language of modern physics, and it appears likely to remain so for the foreseeable future, this situation was certainly not true as recently as a century ago. To emphasize these multicultural roots of mechanics, I have not given literal translations of quotations in French, German, and Italian -- although I have done so for Greek, Latin, and Russian because of relative unfamiliarity with these languages.
I have also included cross-cultural references to topics such as the catenary, the arch, the Huygens pendulum, coin tossing, the Foucault pendulum, the capstan, Plutinos and the Botafumiero. Since topics such as these can easily be explored and studied more closely with standard search engines on the internet, I felt that it was sufficient merely to mention these subjects, without elaborating in detail.