Complete solution of a problem on motion of rigid body around a fixed point in Euler case (Q2703290)

The authors obtain a new parametric solution to the problem of motion of a rigid body around a fixed point which is described by the system of dynamical equations \(J_{\xi}(d\omega_{\xi}/dt)+(J_{\zeta}-J_{\eta})\omega_{\eta} \omega_{\zeta}=M_{0\xi}\), \(J_{\eta}(d\omega_{\eta}/dt)+(J_{\xi}- J_{\zeta})\omega_{\zeta}\omega_{\xi}=M_{0\eta}\), \(J_{\zeta}(d\omega_{\zeta}/dt)+(J_{\eta}-J_{\xi})\omega_{\xi} \omega_{\eta}=M_{0\zeta}\), and by kinematic Euler equations \(\omega_{\xi}=\dot\psi\sin\phi\sin\theta+\dot\theta\cos\phi\), \(\omega_{\eta}=\dot\psi\cos\phi\sin\theta-\dot\theta\sin\phi\), \(\omega_{\zeta}=\dot\psi\cos\theta+\dot\phi\), where \(\psi,\theta,\phi\) are Euler angles, and \(J_{\xi},J_{\eta},J_{\zeta}\) are principal moments of inertia. All possible cases are considered, and Euler angles are determined.