Structure and Interpretation of Classical Mechanics
Classical mechanics experiences a revival with a focus on complex behavior like nonlinear resonances and chaos. A book introduces general methods, mathematical notation, and computational algorithms to study system behavior effectively. It emphasizes understanding motion and nonlinear dynamics through exercises and projects.
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Classical mechanics has seen a resurgence of interest due to the discovery of its rich and complex behavior beyond traditional derivations of equations of motion. This renewed focus includes phenomena like nonlinear resonances and chaotic behavior. The book emphasizes general methods for studying system behavior, regardless of symbolic solvability, using geometric features and computer simulations. It introduces precise mathematical notation and computational algorithms to ensure clarity and avoid ambiguity common in traditional notation. The text encourages active exploration through exercises and projects, leveraging Scheme programming language for computational analysis. By emphasizing understanding motion over deriving equations, incorporating nonlinear dynamics, and using functional notation and computation, the book offers a unique perspective on classical mechanics developed through teaching experience at MIT. The approach aims to enhance comprehension by uncovering and addressing flaws in reasoning, promoting a deeper understanding of mechanics and computation.
6 commentsIt's funny that this quote is not ironic at all, and in fact the authors of SICM include it because they agree with the assessment (by Arnold of his own textbook and its predecessors).
The SICM authors do indeed break with that tradition.
Happy Tau day!
I was surprised by how many ways Sussman and Wisdom found to modernise the Landau and Lipshitz treatment. There is the obvious change, where the first time they solve some equations of motion, it's done numerically, and the solution is chaotic.
There is also a more subtle change, where they keep sneaking in the concepts of differential geometry. The word "manifold" is reserved for a footnote, but if you know what tangent spaces and sprays are, it's straightforward to translate the "local tuples" and see what they're actually talking about.
I think this is a good idea. If physics undergraduates were exposed to manifolds and tangent spaces in their analytical mechanics course, then saw some exterior calculus in their first electromagnetism course, they might be ready for curvature and geodesics when they study general relativity.
The physics is interesting, but SCMUTILS is more interesting. You can:
(1) Write a function
(2) Symbolically compute it's derivative
(3) Render the derivative with LaTeX
(4) Compile the derivative into native code
(5) Integrate out motion using an efficient numerical algorithm
.... all in clean, elegant Scheme. THAT toolset, you can take with you to any domain.