To solve the problem of transverse torques on micro-nano satellites during orbital maneuver, the spin-stabilized method was selected to reduce velocity pointing error. Considering the effects of mass variation and jet damping, the spinning thrusting satellite model which subjected to constant force and zero axial torque was established. After that, the analytic solutions for angular velocity, angular momentum, asymptotic limits of angular velocity and Euler angle were obtained. The example was simulated and the results show that the analytic solutions are highly accurate. Besides, the transverse angular velocity and Euler angle are changing periodically, and the amplitude of transverse angular velocity decreases as the time is increasing. What's more, the curve of angular momentum vector pointing is a circle, and the radius is nearly equal to the satellite velocity increment pointing error. Also, the dynamic unbalance characters of the micro-nano satellite under high spin rate have little influence on the spinning maneuver process. As the micro-nano satellite becomes more disklike, the velocity increment pointing error can be decreased, and the accuracy of the orbit maneuver is raised.