Modelling and Simulation of Physical Systems with Dynamically Changing Degrees of Freedom

Abstract

A new approach is introduced to model and simulate equation-based systems where variables can appear and disappear during simulation without re-generation and re-compilation of code when the numbers of equations and states change during events. The method is presented in a generic, mathematical way and can be in principle applied to all types of declarative, equation-based modelling languages, such as Modelica. A concrete implementation is given for the Julia-based experimental modelling language Modia, which is similar to Modelica. However, Modia features far simpler semantics based on hierarchical collections of name/value pairs and has the ability to support domain-specific algorithms, especially for multibody systems with collision handling. The new method is demonstrated with heat-transfer in a rod, separation of stages of a rocket and gripping operations of a robot.