Core Language Semantics Sample Clauses

Core Language Semantics. ‌ D A Q Modelica models can be described using a 10-tuple ( , , , I , D, A, Q, R, Z, T ), whose components are as follows: • D is a lens denoting the set of dynamic variables, that is variables which are de- scribed by differential equations. • A is a lens denoting the set of algebraic variables, that is variables that do not appear differentiated. • Q is a lens denoting the set of discrete variables. • I is the initialisation predicate, that is the set of initial equations defined in the block. • D is a hybrid relation denoting the set of (conditional) differential equations. • A is a predicate denoting the set of (conditional) algebraic equations. • Q is a predicate denoting the set of (conditional) discrete equations. • R is a set of relations, each denoting a (conditional) reset equation. • Z is a set of expressions, each denoting a zero-crossing function that can trigger a state event. • T is a predicate denoting when time events can occur. D A Q Lenses , , and partition the continuous state c and thus specify all variables that are characterised by the model’s trajectory. ∧ − D { } A ∅ Q ∅ For the bouncing ball example, we have = h, v , = , and = , since there are only dynamic variables in that model. Then we have I = (v = 0 h = 2.0) for the initialisation, and D = (h has-der v v has-der ( 9.81)) for the differential equations. There are no algebraic or discrete equations, and so A = Q = true – that is, there are no constraints imposed. There is a single conditional reset equation which updates the ball’s velocity upon impact, and so we have:
Sample 1
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