Classical Mechanics Fall 2024 Lecture 1: Newton's Laws

In this lecture, we cover Newton's laws of motion and the concept of reference frames.
Sources on Newton and the Principia:
[1] De Gandt, F. (2014). Force and geometry in Newton's Principia (Vol. 312). Princeton University Press.
[2] Cohen, I. B., & Whitman, A. (1999). The Principia. Newton. A New translation.
[3] Buchwald, J. Z., & Fox, R. (Eds.). (2013). The Oxford handbook of the history of physics (Vol. 48). OUP Oxford.
[4] Janiak, Andrew, "Newton’s Philosophy", The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), Edward N. Zalta (ed.)
[5] Linsky, Bernard and Andrew David Irvine, "Principia Mathematica", The Stanford Encyclopedia of Philosophy (Fall 2024 Edition), Edward N. Zalta & Uri Nodelman (eds.)
Edit: There is an error when I discuss non-inertial transformations. The matrix "At" should in fact just be a matrix "R(t)" that represents constant rotation; its exact form depends on the dimension, but it is not a linear function of t.
Edit 2: I should clarify: Newton did not surprise Halley by surmising that planets orbit in ellipses (Kepler had made the same assertion at the beginning of the century), but rather by claiming he could prove they orbited in ellipses.

[@nahiarabeer9565]

Your writing made me surprised 😮