  Hybrid systems are characterized by the hybrid evolution of their state: A
part of the state changes discretely, the other part changes continuously over
time. Typically, modern control applications belong to this class of systems,
where a digital controller interacts with a physical environment. In this
article we illustrate how a combination of the formal method VDM and the
computer algebra system Mathematica can be used to model and simulate both
aspects: the control logic and the physics involved. A new Mathematica package
emulating VDM-SL has been developed that allows the integration of differential
equation systems into formal specifications. The SAFER example from Kelly
(1997) serves to demonstrate the new simulation capabilities Mathematica adds:
After the thruster selection process, the astronaut's actual position and
velocity is calculated by numerically solving Euler's and Newton's equations
for rotation and translation. Furthermore, interactive validation is supported
by a graphical user interface and data animation.
