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The current paper describes how quaternions are used successfully and effectively in simulations of unmanned aerial vehicles (UAVs) and satellite motion through definition of the UAV airframe or satellite body as a rigid body. By such means the authors try to raise interest among students and scientists in the mathematical formalism of quaternions that was very popular more than 100 years ago, but was replaced by vectors and matrices. Nevertheless, quaternions benefits make them valuable in numerous tasks, among others the numerical integration of rigid body motion dynamics equations.Simulations, part of the current project, can be viewed on http://ialms.net/sim/ web address.

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