“能量穿梭机”实验中的类星体运动

Study on similar celestial movement in energy-transfer machine

通过理论分析建立动力学方程,用四阶Runge-Kutta进行求解,研究了"能量穿梭机"实验仪中的类星体运动.不考虑阻力时,小球会进动并且进动角随圆锥面倾斜角的增大而减小,当倾斜角约为55.6°时,进动消失,小球做类似星体的椭圆运动.考虑阻力时,由于能量损失小球的运动不再有周期性,这与小球在圆锥面上的真实运动相符.

Based on New tonian mechanics ,the dynamic equations of the ball were established and the numerical solution was got by the forth order Runge‐Kutta method .To be more specific ,two models were built under ideal and non‐ideal conditions ,respectively .In the first model ,air resistance was neglected .A precession of the orbit of the ball was found .Moreover ,the angle of precession would decrease with the increase of the obliquity of the cone .When the latter approaching a particular value of approximately 55 .6° ,the precession vanished and the ball had an elliptic orbit .In the second model ,the resistances were set to be proportional to velocity in view of the low velocity .According to the experiments ,the motion of the ball was aperiodic due to the loss of energy ,which was consistent with the real situation .