The free motion of a rigid body carrying a rotating mass without change of the centroid (this system may be called one-rotor gyrostat) is discussed. Equations of motion are derived: first integrals as a vectorial equa...The free motion of a rigid body carrying a rotating mass without change of the centroid (this system may be called one-rotor gyrostat) is discussed. Equations of motion are derived: first integrals as a vectorial equation which contained the right vector of an angular velocity of the given rotor with respect to the carrier body and the turn-tensor of this body;a scalar relation between rotation angle of the given rotor with respect to the carrier body and the angular velocity of the carrier body. Only two of these parameters are independent variables. To get equations and to exclude the singular points in the solutions, it is necessary to determine the turn-tensor of the carrier body in the most suitable form. To this end the representation theorem of the turn-tensor and some additional arguments are used. As a final result, we enabled to get two complicated differential equations of the first order. In particular case, the exact solution is represented. Excluding the singular points numerical solutions are determined.展开更多
文摘The free motion of a rigid body carrying a rotating mass without change of the centroid (this system may be called one-rotor gyrostat) is discussed. Equations of motion are derived: first integrals as a vectorial equation which contained the right vector of an angular velocity of the given rotor with respect to the carrier body and the turn-tensor of this body;a scalar relation between rotation angle of the given rotor with respect to the carrier body and the angular velocity of the carrier body. Only two of these parameters are independent variables. To get equations and to exclude the singular points in the solutions, it is necessary to determine the turn-tensor of the carrier body in the most suitable form. To this end the representation theorem of the turn-tensor and some additional arguments are used. As a final result, we enabled to get two complicated differential equations of the first order. In particular case, the exact solution is represented. Excluding the singular points numerical solutions are determined.
