In these two talks, I will discuss how various classes of mechanical processes can be described using categories of relations (the semantics), which come equipped with "ZX-calculus" style graphical languages (the syntax). In the first talk, I will review how affinely-constrained mechanical systems with discrete positions and momenta are modelled using the category of affine Lagrangian relations. I will give examples in both quantum and classical mechanics, and I will sketch the associated family of graphical languages. In the subsequent talk, I will discuss how the syntax and semantics can be extended with discrete-time-evolution exploiting the theory of feedback monoidal categories, profunctors, and sesquilinear forms.