High-precision representations of inertial rotations and louis poinsot instability

The coordinate method for determining the rotations of bodies in space is proposed. The method does not use Euler angles and hypercomplex Hamilton numbers. The developed computational technique is based on the point distribution of masses in space. If the body is replaced by a system of points and this approximation is sufficient, then the rest of the calculation results are highly accurate. The latter is achieved through the synthesis of an exact method for solving systems of algebraic equations with a high-precision step-by-step method for solving systems of differential equations resolved with respect to the derivatives of the desired quantities. Based on the developed computational method, unstable inertial rotations were studied. The existence of an instability different from the Louis Poinsot instability is shown.