I was trying to find some references for modelling the equations of motion of a simple dynamical system (say a pendulum on a moving mass) when I realized that the very vast majority of the material you find online or even in textbooks suffer from the following problems:
Reference frame poorly defined, wildly assigned or even implicit. No idea which point is considered to be origin, which direction positive, etc.
Free body diagram completely unprincipled and/or confusing.
Confusion between magnitude of a vector (e.g., Force) and the vector itself (not mentioning switching back and forth)
No general form for basic laws of motion. Sometimes when the authors apply Newton's second law, for instance, they are applying it implicitly along some dimension.
Constants are stated and used without derivation or motivation, e.g., moment of inertia are mysterious constants that you would look up from a table
And many more problems.
Does there exist any textbook on modeling classical dynamical systems (pendulum, masses, multi-link robot) from scratch?
The field of analytical mechanics is devoted to this. Most prominently, the Lagrange formalism, the Hamilton formalism, and the Hamilton–Jacobi formalism are ways to deduce equations of motion in a systematic manner.
Analytical mechanics is usually a major part of courses on theoretical mechanics, which are part of the standard physics curriculum (at least in my country). Any decent textbook on theoretical mechanics should therefore at least be a good starting point on this topic.