Kinematics and Dynamics for Practicing Engineers Lecture 13: An Exegesis of Newton’s Second Law

Discipline: Flight Mechanics Abstract: Although the famous equation F = ma (or its scalar equivalents) is attributed to Newton, no form of this equation can be found anywhere in his 1687 magnum opus Mathematical Principles of Natural Philosophy (usually called the Principia and pronounced Prinkipia from the Latin). Scalar versions of the equation do, however, appear in a 1749 paper by Euler, but with a mysterious 2 in each of the expressions. In this talk, a possible solution of the mystery is put forth. One often encounters statements to the effect that Newton’s Second Law of Motion fails to provide correct descriptions of the motion of a particle in non‐Newtonian reference frames. Such statements are misleading and reflect fuzzy thinking on the part of those who make them. In the second part of this talk, the case is made, and illustrated with an example, that Newton’s Second Law governs the motion of a particle in any reference frame, and that proper use of sufficiently explicit notation can prevent the conceptual error that leads to the opposite conclusion. About the Speaker: David Levinson has 47 years of experience as a dynamicist in the space industry, where he has been responsible for producing special purpose computer programs for simulating motions of complex mechanical systems, such as multibody spacecraft, robotic devices, and aerospace mechanisms. Mr. Levinson, currently retired, was employed at Lockheed Martin (formerly Lockheed Missiles and Space Company) from 1977 to 2013, and at Maxar Space Systems (formerly Space Systems Loral) from 2013 to 2024. Over the years, Mr. Levinson has been the recipient of numerous engineering awards, among them the American Institute of Aeronautics and Astronautics (AIAA) San Francisco Section Outstanding Young Engineer Award, the AIAA San Francisco Section Engineer of the Year Award in Astronautics, the AIAA San Francisco Section Engineering Educator of the Year Award, the American Society of Mechanical Engineers (ASME) Santa Clara Valley Section Distinguished Mechanical Engineer Award, the American Astronautical Society (AAS) Outstanding Achievement Award, and the Lockheed Missiles and Space Company President’s Award. Mr. Levinson is the author or coauthor of 43 published technical papers, and a coauthor of the two McGraw-Hill textbooks, Spacecraft Dynamics and Dynamics: Theory and Applications, as well as four desktop-published mechanics textbooks. He is also the author of the desktop-published undergraduate textbook Dynamics for Engineering Analysis. Mr. Levinson is a Fellow of both the AAS and the ASME, and is an Associate Fellow of the AIAA. As a participant in the Discover “E” K-12 engineering outreach program for more than 20 years, he has given 270 classroom presentations to middle school and high school students and teachers about careers in engineering. He is a popular speaker, and was an ASME Distinguished Lecturer from 2000 through 2004. For more than forty years he has lectured on technical subjects to a wide variety of audiences, including Cub Scouts, fifth graders, swimming coaches, middle school and high school students, school teachers, Kiwanis and Rotary clubs, physicians, practicing engineers, engineering graduate students, and university professors.

David Levinson

9/8/2025 8:00:00 PM