Do you have the print edition? 75The procedure solve-linear-left multiplies its second argument by the inverse of its first argument on the left. I think that's doubly true here. The range of this new function is itself a structure with the same number of components as the argument with respect to which the function is differentiated. QM looks like classical under many macro situations. In that book Feynman DID NOT claim that the theory of Quantum Mechanics implies the PLA for classical mechanics, relativity or EM. I have a hard copy of the first edition. Of course, actual bodies are never truly rigid, so we may wonder what detailed approximations have to be made to treat them as if they were truly rigid. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. Points are added to the plot with the procedure plot-point that takes a plot window and the abscissa and ordinate of the point to be plotted. It would be a lot of work, and some of the type decisions that would be needed would probably complicate the UX of the software (the automatic differentiation of functions of various shapes would make typing the D operator interesting; I think it would force all real-valued functions of a real variable to look like they were working in a vector space of dimension 1, or the inconsistency would be maddening). 47The derivative or partial derivative of a function that takes structured arguments is a new function that takes the same number and type of arguments. I'm resurrecting this project since I bought the second edition of the book. 73We may encounter singularities that make this matrix uninvertable, but in real systems these singularities are isolated and can be avoided by changing coordinates. If nothing happens, download Xcode and try again. This second edition is from 2015, following the 2001 first edition. Second stage: ). 86Traditionally the Jacobi constant is defined as CJ = −2ℰ. If that is the case you are confusing the expectation value of a physical quantity in QM with an actual physical measurement. Nice little talk! 94This constraint has the same form as those used in the demonstration that L = T − V can be used for rigid systems. 97We will see in chapter 2 how to compute the kinetic energy of rotation, but for now the answer is 12M R2θ˙2. I have an educational resource for introduction to Hamilton's stationary action. The deep mystery is always why does nature work the way it does. Oh interesting! In particular, note that the constraint terms do not add up to a potential energy with a minimum when the constraints are exactly satisfied. Here's my attempt at applying Andres Raba's wonderful SICP layout (. My contact details are in my profile. The true trajectory has the following obvious property: at every instant in time the rate of change of potential energy matches the rate of change of kinetic energy. The procedure principal-value is used to reduce an angle to a standard interval. Structure and Interpretation of Classical Mechanics. Euler's theorem says that if f is a homogeneous function of degree n, then Df(x)x = nf(x). We do not consider the singular cases here. So, if u = Mv then v = M−1u; (solve-linear-left M u) produces v. 76The Scmutils system provides a variety of numerical integration routines that can be accessed through this interface. You dont need QM to formulate, derive or use the LAP. A constant multiple of a function is the function whose value is the constant times the value of the function for each argument: cf is the function t ↦ cf(t). 41There are lots of good ways to make such a parametric set of approximating trajectories. The copy on Library Genesis does indeed seem to contain that license, but someone could have added that when they uploaded it to libgen: The Google Books copy that MIT Press links to as the "Preview" includes the CC license: There's a ton to learn from this book, especially if both Scheme (or functional programming in general) and the Lagrangian and Hamiltonian formulations of mechanics are new to you as they were to me when I first came across the text online.