What does "symbolically tractable" mean in the following quote?
"Traditional treatments of mechanics concentrate most of their effort on the extremely small class of symbolically tractable dynamical systems." from the Preface of Structure and Interpretation of Classical Mechanics
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"Tractable" means feasible, possible, solvable, workable, able to be handled.
"Symbolically" (in this context) means by use of algebra (symbols and elementary functions), as opposed to numerical methods.
So, a dynamical system is "symbolically tractable" if it can be solved by algebraic methods, rather than numerical ones. As the author implies, only a very small fraction of real-world dynamical systems can be handled this way.
Meaning they have an explicit solution that can be written with symbols, using some array of known elementary functions and special functions, as opposed to a numerically approximate solution.