The thesis presents the physics and mathematics necessary for the realization of the physics engine, suitable for use in real-time applications. In the development process we have focused on computer games and therefore have taken into account the limitations and pitfalls that can arise in such a case. We start by presenting the purpose and use of physics engines and also mention already existing solutions. We get to know with particles without mass, which enable us to realize ballistics, forces in general and springs, as a special type of them. Then we confront the hard constraints such as collision detection, resolving collisions in the case of collisions of bodies and their movements in such situations. This gives us a mass aggreg...