"Sussman and Wisdom make a bold experiment in communicating mathematical physics: they say exactly what they mean. Even a computer can follow their equations. By using this textbook, students painlessly master Scheme, a minimalist programming language, at the same time. This empowers them to go beyond the simplistic integrable systems that dominate the traditional course, to the richness of nonlinear resonance and chaotic dynamics. The hard core of rigor is softened by a personal and enthusiastic writing style"
It's a great resource but I don't think SICM is quite comparable to SICP because it's not aimed at complete beginners. If you know or remember nothing about Physics it will be a tough read and you'll be lost quickly.
Personally I like the Theoretical Minimum lectures [0] - they are very clear and concise.
When reading Feynman, don't miss the fact that the original audio recordings are now freely available [1], which, even speaking as someone with a strong preference for reading vs. listening or watching instructive material, shouldn't be missed. Feynman's sheer enthusiasm for the material is hard to get across in print.
In the spirit of SICP, I also like Spivak's less conventional Physics for Mathematicians [2], but, as the title suggests, this assumes more, or at least different, mathematical prerequisites than most introductory mechanics texts. "Strong undergraduate maths background — at least one course each in linear algebra and differential equations, say, or equivalent self-study — with a bit of motivated extracurricular work in differential geometry" sounds about right, but here I'm basically just describing my own background when approaching the book, so YMMV.
Structure and Interpretation of Classical Mechanics
https://mitpress.mit.edu/books/structure-and-interpretation-...
...with Gerald Sussman as one of the authors. The Feynman Lectures on Physics might be what you are looking for:
https://www.feynmanlectures.caltech.edu/