Modelin of a generic underwater vehicle with MathModelica

Modeling is an important element of the research at the Department of Autonomous Systems at the Swedish Defence Research Agency. Several different modeling languages for different purposes are used. Modelica is relatively new object-oriented modeling language that uses an acausal approach instead of the causal approach traditionally used. Rigid body motion and a fluid are two examples of dynamical systems. A rigid body immersed in a fluid is two dynamical systems that interacts. These two systems are described as one single dynamical system according to Kirchhoff. A general remarkably compact mathematical form is derived to describe the combined body+fluid system. This form is implemented in the modeling language Modelica. The particular modeling problem is solved in two different ways. The resulting developed model is integrated with the Modelica Additions MultiBody library which makes it possible to model arbitrary internal dynamics and the change of body configuration is simple. The developed flexible tool is used to model a generic underwater vehicle with internal propulsion and actuation. Mirror symmetry and discrete rotational symmetry are studied and the invariance of the total kinetic energy of the body+fluid system is used to relax the problem of finding additional body properties due to the fluid. The symmetries put constraints on the property tensors that must conform to certain structures. By performing simulations the knowledge about how the body+fluid system behaves depending on the mathematical structure of the property tensors is increased. That internal propulsion and control is possible is shown explicitly in the simulations.