The dynamical simulation method of the Lagrange's top proposed in [1] can be applied to nonsymmetric Euler's top in free motion. In application of the method, the invariant angular momentum is used to derive non-dimensional equations. To cancel integral error which central difference scheme accumulates, total derivative of the first integral is applied. For the evaluation of numerical precision, analytical solution of a symmetric Euler's top is utilized. The study case of the simulation is free rotation around near z-axis which is stable.

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  The restarted GMRES(k) method is an effective means for solving linear systems of equations where the coefficient matrix is nonsymmetric. The incomplete LU factorization without extra fill-ins is a widely used preconditioning. Sometimes this preconditioning works well. However, sometimes it does not work well at all. We propose an efficient and robust preconditioning technique based on iteration matrices of stationary methods, e.g., Gauss-Seidel and SOR methods. Through numerical experiments, we verify the effectiveness of the proposed preconditioning.

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