Euler–Poisson equations of a dancing spinning top, integrability and examples of analytical solutions

Improved Equations of the Lagrange Top and Examples of Analytical Solutions

“…This implies that the position of the laboratory system is completely fixed, as described above. If for some reason we want to choose a different coordinate system, we will be forced to use Equation (10) with the symmetric matrix (12) containing non-zero off-diagonal elements instead of a diagonal matrix (14). Notice that the failure to take this circumstance into account leads to a lot of confusion; see [22].…”

“…Because this is a somewhat surprising observation, its validity and comparison with the literature are carried out in detail at the end of Section II and in Section IV. Being one of the classical problems of nonlinear dynamics and integrable systems, this issue, however, is of interest in the modern studies related with construction and behaviour of spinning particles and rotating bodies in external fields beyond the pole-dipole approximation [11][12][13][14][15][16][17][18][19].…”

Tetama nas matas mineiras: sítios Tupi na microrregião de Juiz de Fora - MG

“…This was achieved by reducing the original problem to the problem of the motion of a one-dimensional harmonic oscillator under the action of a constant external force. This method also allows one to find particular solutions in elementary functions in several more complex problems, including the cases of dancing top [10], Lagrange top [7] and free symmetric body in stationary and homogeneous electric and magnetic fields [11].…”