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The numerical integration plays a fundamental role in understanding thebehaviour of many mechanical systems. In this paper some important aspects ofthe mechanical integrators on the dynamics of a mechanical system are studied.More specific, we have shown that if that the Lie-Trotter integrator isobtained, in case of Euler equations for the dynamics of symmetric free rigidbody, then it is a Poisson integrator. At the end of the paper some importantremarks are presented.

The Lie-Trotter integrator in the dynamics of the symmetric free rigid body