Abstract
Dynamics is the theory of motion and the forces and torques that produce it. This theory integrates our earlier studies of kinematics, the geometry of motion, with certain fundamental laws of nature that relate force, torque, and motion. In this chapter the primitive concepts of mass and force introduced in Chapter 1 are related to motion through some basic principles commonly known as Newton’s laws. Sir Isaac Newton (1642–1727) in his Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), often referred to as simply the Principia, published in 1687, formalized and extended earlier achievements of others by creating an axiomatic structure for the foundation principles of mechanics. By the organization of problems around his fundamental laws, Newton successfully demonstrated the application of his theory to the study of problems of mechanics of the solar system. He thus began the idea that the motions of bodies may be deduced from a few simple principles.
I would mention the experience that it is exceedingly difficult to expound to thoughtful hearers the very introduction to mechanics without being occasionally embarrassed, without feeling tempted now and again to apologize, without wishing to get as quickly as possible over the rudiments and on to examples which speak for themselves. I fancy that Newton himself must have felt this embarrassment… Heinrich Hertz The Principles of Mechanics
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
BARTLETT, A. A., Are we overlooking something? 1981 Robert A. Millikan Lecture, Steven’s Point, Wisconsin, June 17, 1981. American Journal ofPhysics 49, 1105–19 (1981). The problem of U.S. Navy torpedo failures and its simple explanation are described. See also Bartlett’s earlier article, An effect of friction in an accelerated system, American Journal of Physics 37, 665–6 (1969).
BERLINSKI, D., Newton’s Gift, Free Press, New York, London, 2000. The author begins with the ordinary aspects of Newton’s childhood, sketches his student years, and describes his professional life at Cambridge. The ultimate focus, however, is on Newton’s creation of the calculus and his remarkable masterpiece, his supreme gift—the Principia, published in 1687—wherein the principles of rational mechanics and the law on universal gravitation are created and the results demonstrated in describing the motions of planets. Remarks on Newton’s theory of light, his experiments on optics, his development of the reflective telescope, and his quarrel with Robert Hooke provide additional interesting reading.
BIXBY, W., The Universe of Galileo and Newton, American Heritage, 1st Edition, New York, 1964. The writer presents a well-illustrated sketch of the life and scientific accomplishments of Galileo Galilei (1564–1642) and Isaac Newton (1642–1727) in describing and explaining the motions of bodies in the universe.
BOWDEN, F. P., and TABOR, D., The Friction and Lubrication of Solids (2 volumes), Clarendon, Oxford, 1950. A much abbreviated introduction to this major treatise on the mechanism of friction may be found in their more elementary monograph Friction and Lubrication, Methuen’s Monographs on Physical Subjects, Methuen and Co., London, 1967.
CAJORI, F., Newton’s Principia. A well-known English translation of Mathematical Principles of Natural Philosophy by Isaac Newton, 1687. University of California Press, Berkeley, 1947. The wide recognition of Newton’s monumental work derives mainly from the famous axioms, or laws of motion, presented in the first of the three books. Newton’s style anticipates readers having a strong foundation in geometry, even though his calculus had been developed earlier.
CHANDRASEKHAR, S., Newton’s Principia for the Common Reader, Oxford University Press, New York, 1995. The author presents a comprehensive study of the Principia in contemporary language and the methods of analysis by the calculus to take the reader through the chain of argument leading to Newton’s formulation of his universal law of gravitation.
DERESIEWICZ, H., Amontons and Coulomb, friction’s founding fathers. In: Approaches to Modelling Friction and Wear, editors F. F. Ling and C. H. T. Pao, Springer-Verlag, New York, 1986, pp. 50–60. Amontons’s report to the French Academy and its response are outlined, and Coulomb’s comprehensive investigation is discussed briefly. References to original works may be found here.
DURRELL, C. V., Readable Relativity, Harper and Brothers, New York, 1960. Written by a teacher of mathematics and a master of the subject, this little book presents an entertaining introduction to relativity. Simple mathematical arguments provide the general reader with a clear exposition of the basic principles of Einstein’s theory.
EINSTEIN, A., Relativity, The Special and the General Theory, Crown Publishers, New York, 1961. A simply written, popular exposition on the relation of the theory of relativity to Newton’s classical theory of motion and gravitation. The special theory compares observer experiences in frames having uniform relative motions, while the general theory admits all possible frames having nonuniform and curvilinear relative motions. The special theory is based upon two axioms: (1) the laws of nature in every material universe have the same form for all observers in uniform relative motion, and (2) the speed of light emitted by a body at rest or in uniform motion is the same for all observers.
FERNIE, J. D., The neptune affair. American Scientist 83, No. 2, 116–9 (1995). The intrigue of Neptune’s discovery is reviewed here. Though credited with the discovery of Neptune, Le Verrier was not the first to predict its location. In September 1845, the British mathematician John Couch Adams presented calculations that predicted within less than 2o the place in the sky where the planet might be found as of October 1, 1845. The incredible arrogance of Adams and the Astronomer Royal, George Airy, blocked further communication and publication of Adams’s more precise prediction of Neptune’s location, while details of Le Verrier’s work appeared later in the Comptes Rendus of the French Academy of Sciences. Le Verrier’s final paper on the topic reached England on September 29,1846; it gave Neptune’s mass and coordinates within only a few degrees of Adams’s prediction. The concluding irony of the story, however, is that Galileo had twice recorded in his notebooks during the period December 1612 to January 1613, almost 234 years earlier, diagrams of telescopic observations that show a “fixed star” drawn on a directed line from Jupiter in the plane of its satellites. A more recent review by astronomers in 1980 of Galileo’s observations revealed that he had actually discovered Neptune. Due to the poor resolution of his telescope, however, he identified it as a star.
FERNIE, J. D., In pursuit of Vulcan. American Scientist 82, No. 5, 412–5 (1994). The history of the search for Vulcan, the hypothetical planet thought to be somewhere between Mercury and the Sun, is outlined.
FRANK, P., Philosophy of Science—The Link Between Science and Philosophy, Prentice Hall, 1957. The logical structure of Newton’s laws of motion and their related operational foundation are discussed in Chapter 4.
HART, I. B., The Mechanical Investigations of Leonardo da Vinci, University of California Press, Berkeley, 1963. This is a fascinating historical study of da Vinci, not as an artist but as a student of mechanics. Leonardo’s personality, strange habits, and his creative genius in conceiving unusual applications of the mechanics of his time, and in some measure contributing to it through his mechanical investigations, are graphically described. A wealth of interesting historical references may be found here. See also the critical Forward by E. A. Moody. Leonardo’s notes on friction are described in Chapter VI. The quotation on page 1 above is cited in Chapter V, p. 78
HEISKANEN, W. A., and VENING MEINESZ, F. A., The Earth and its Gravity Field, McGraw-Hill, New York, 1958. The gravity field, the shape and other features of the Earth, the international gravity formula, and various static and dynamic gravity-measuring methods are described in Chapters 3 and 4.
HERTZ, H., The Principles of Mechanics. Dover, New York, 1956. The author focuses on providing a philosophical and mathematical foundation for the kinematics and dynamics of material systems in development of the theory of mechanics. There are no worked examples in the text.
HUBBERT, M. K., and RUBEY, W. W., Role of fluid pressure in mechanics of overthrust faulting. I. Mechanics of fluid filled porous solids and its application to overthrust faulting, Bulletin of the Geological Society of America 70, 115–66 (1959). The sliding can experiment, attributed to M. A. Biot, is related to gravitational sliding of fault blocks due to interstitial fluid pressure that allows low angle thrust faults to occur under shear stress of only moderate magnitude. The application of the principle to the design of bearings for the Mount Palomar telescope is described by Karelitz, M. B., Oil pad bearings and driving gears of the 200-in. telescope, Mechanical Engineering 60, 541–4 (1938). Several further references may be found here. See also Noble, B., Applications of Undergraduate Mathematics in Engineering, Macmillan, New York, 1967. Equilibrium analysis of the sliding can experiment is described in Chapter 8, pp. 166–8.
KANE, T. R., Analytical Elements of Mechanics, Academic, New York, 1959. Volume 1 concerns statics. A parallel discussion of gravitational and contact forces, including several worked examples, may be found in Chapter 4.
KRIM, J., Friction at macroscopic and microscopic length scales. American Journal of Physics 70, 890–7 (2002). This paper provides a useful summary and extensive guide to a variety of resources on the fundamentals of friction. Traditional concepts on the origin of friction and modern molecular theories are presented.
LONG, R., Engineering Science Mechanics, Prentice-Hall, Englewood Cliffs, New Jersey, 1963. The author adopts Mach’s approach in setting down the foundation postulates of Newton’s mechanics. Coulomb friction, gravitational attraction by a sphere, Newton’s law in the noninertial Earth frame, and other topics are presented.
MORISON, Admiral S. E., The Two-Ocean War, A Short History of the United States Navy in the Second World War, Little-Brown, Boston, Toronto, 1963. This book, based on the author’s fifteen-volume History History of the United States Naval Operations in World War II, covers the most important battles and campaigns of the two-ocean war. Brilliant contributions of engineers, mathematicians, and scientists to the design, development and efficient use of military devices and equipment for the American and British Armed Forces are described, pp. 125–130. Such questions as—“What pattern of depth charges at what settings has the best mathematical chance of killing a submarine?”—were addressed. During the critical early months of the Pacific war, however, the Navy learned the hard way that its torpedoes were gravely defective and that Japanese torpedoes were more powerful, faster, had a greater range, and were more efficient machines of destruction than its own, pp. 12–13.
MURPHY, D., Hit or Miss. American Heritage of Invention and Technology 13, No. 4, 56–63 (1998). The frustrating effects of U.S. Navy torpedo failures and the solution of the problem is described.
NOLL, W., On Material Frame-Indifference, Carnegie Mellon University, Center for Nonlinear Analysis, Department of Mathematics, Technical Report No. 95-NA-022, November 1995, 10 pages. See also Chapter 1 (pages 13–22) of the same title in Noll’s recent comprehensive work 5 Contributions to Natural Philosophy, Center for Nonlinear Analysis, Department of Mathematical Sciences, Research Report No. 04-CNA-018, October 2004, 73 pages. In these reports the author presents a thorough, lucid discussion of the principle of material frame indifference, a lexicon of earlier terms used to characterize it is included, and its application to the internal interaction between two particles is illustrated. The text illustration parallels that due to Noll. A similar derivation was first reported in Noll’s article On the Foundation of the Mechanics of Continuous Media, Carnegie Institute of Technology, Department of Mathematics, Technical Report No. 17, June 1957, 68 pages (see pages 38–40).
RAMSEY, A. S., Newtonian Attraction, Cambridge University Press, Cambridge, Massachusetts 1961. This is an intermediate level introduction to the theory of potential based on Newton’s law of gravitation. Attraction by a sphere is studied in Chapter III, and the difficult problem of attraction by an ellipsoid is described in Chapter VII. Additional examples and problems of scaled difficulty may be found here.
ROSCOE, T., Pig Boats, Bantam Books, New York, 1982. This is a comprehensive account of U.S. Pacific Fleet submarine operations during World War II written principally for the Bureau of Naval Personnel based on both U.S. and Japanese naval records and submarine patrol reports. Countless torpedo malfunctions were reported during the critical early months of the war. Chapter 9 recounts, for example, the submarine Grenadier’s sinking of the large Japanese passenger liner Taiyo Maru that was transporting a group of Japanese scientists and other experts, most of whom went down with the ship en route to conquered territories in the East Indies. Lieutenant Commander “Pilley” Lent, however, reported that two of the four magnetically triggered torpedoes fired on Taiyo Maru were duds or malfunctioned. Frequent problems of unreliable state-of-the-art magnetic exploders that sometimes exploded prematurely, and sometimes not at all, ultimately led to the use of older impact exploders. Chapter 11, Torpedo!, tells of the serious effects of disturbing torpedo impact failures (including Tinosa’s failed attack on the Tonan Maru), their cause and ultimate elimination. These major technical problems of defective magnetic and impact torpedoes and the drop-test experiments leading eventually to the solution of the latter are depicted, though somewhat loosely, in the 1951 Warner Brothers film Operation Pacific, starring John Wayne and Patricia Neal.
SNYDER, G. S., The Royal Oak Disaster, William Kimber, Great Britain, 1976; reprinted by Presido Press of San Rafael, California, 1978. An American journalist describes in this book one of the worst disasters in the history of the Royal Navy, which occurred during the early months of World War II. The story is a fascinating account of the sinking of the great battleship Royal Oak by the German submarine U-47, under Lieutenant Commander Gunther Prien, following his remarkable intrusion into the supposedly impregnable British naval base at Scapa Flow.
SYNGE, J. L., and GRIFFITH, B. A., Principles of Mechanics, 2nd Edition, McGraw-Hill, New York, 1949. Chapters 5 and 13 study effects of the Earth’s rotation on the apparent gravitational field strength and on the equation of motion.
TRUESDELL, C., Essays in the History of Mechanics, Springer-Verlag, Berlin-Heidelberg-New York, 1968. This is a fascinating collection of lectures by a renowned scholar, applied mathematician, and historian of mechanics—highly recommended to all readers. Chapter 1 describes and critiques the notebooks and the mechanics of Leonardo da Vinci, including his law of friction and study of motion on an inclined plane. The development of the foundation principles of classical mechanics in the 17th and 18th centuries due to Newton (1687), Euler (1750), Lagrange (1788), and others is detailed in Chapter 2. See also Reactions of late Baroque mechanics to success, conjecture, error, and failure in Newton’s Principia. In: Mechanics, editor N. C. Lind, American Academy of Mechanics, University Park, Pennsylvania pp. 1–47, 1970. Euler’s papers of 1744–1750 are sketched in The Rational Mechanics of Flexible or Elastic Bodies 1638–1788. Introduction to Leonardi Euleri Opera Omnia, Vol. 10 and 11, 2nd Series, pages 222–9, 250–4, Orell Füssli Turici, Switzerland, 1960. This is a historical study of the mechanics of deformable bodies ideal for all students of engineering and applied mathematics.
TRUESDELL C., and NOLL, W., The Non-Linear Field Theories of Mechanics, Flügge’s Handbuch der Physik, Vol. III/3, New York, 1st Edition 1965, 2nd Edition Springer-Verlag, Berlin, Heidelberg, 1992. The principle of material frame indifference is presented in Sections 17 through 19, pages 41–5, and the history of the principle is traced in Section 19A, pages 45–7, of the first edition.
YEH, H., and ABRAMS, J. I., Principles of Mechanics of Solids and Fluids. Vol. 1, Particle and Rigid Body Mechanics, McGraw-Hill, New York, 1960. Equipollent force systems are discussed in Chapters 4 and 5.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Beatty, M.F. (2006). The Foundation Principles of Classical Mechanics. In: Principles of Engineering Mechanics. Mathematical Concepts and Methods in Science and Engineering, vol 33. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31255-2_1
Download citation
DOI: https://doi.org/10.1007/978-0-387-31255-2_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-23704-6
Online ISBN: 978-0-387-31255-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)