Newton’s Principia for the Modern Student

Beschrijving

At some point in their careers, most physicists make an attempt to read and understand Newton’s Principia. Unfortunately, it is an extremely difficult book — it quickly becomes clear that one does not simply ‘read’ the Principia. Even for a professional physicist, Newton’s prose (written in Latin and translated to English) is difficult to follow. His diagrams and figures are complicated and confusing. To understand fully what Newton had done, the problems he posed would have to be solved by the reader.

Newton’s geometric methods and techniques, and the geometry and vocabulary that passed for common knowledge in the late 17th century, are now arcane and all but inaccessible to a modern reader. The contents of the Principia are not. Most physicists and physics students, and many scientists in general, would find the physics in the Principia interesting, illuminating, and useful.

This book presents all the wonderful physics in the Principia in a manner that a modern reader can recognize and understand, using physics and mathematics as we understand them in the 21st century.

Contents:

• Preface

• Acknowledgements

• Introduction to the Principia

• Newton’s Principia:

  • Definitions
  • The Laws of Motion

• The Motion of Bodies:

  • The Method of Limits and Ratios
  • Finding Central Forces
  • Conic–Section Orbits
  • Finding Conic–Section Orbits Given a Focus
  • Finding Orbits When no Focus is Given
  • Finding Motion in Given Orbits
  • Rectilinear Ascent and Descent
  • Finding Orbits for any Central Force
  • Precessing Orbits
  • Constrained Motion
  • Objects Attracted by Central Forces
  • Attractive Forces of Spherical Bodies
  • Attractive Forces of Non-Spherical Bodies
  • Motion of Minimally Small Bodies

• Motion in Resisting Media:

  • The Linear Resistive Force —bν
  • The Quadratic Resisting Force —kν2
  • The Resisting Force —bν — kν2
  • Circular Orbits in Resisting Media
  • The Density and Compression of Fluids
  • Simple Pendulums with Resisting Forces
  • The Motion of Fluids
  • Wave Motion through Fluids
  • The Circular Motion of Fluids

• The System of the World:

  • Introduction
  • Rules for the Study of Science
  • Phenomena
  • Propositions of Book III
  • General Scholium

• Epilogue:

  • Newton’s Principia for the Modern Student
  • References
  • Index

Readership: Undergraduate students of physics and mathematics, as well as academics and engineers.