Juggling a devil-stick can be described as a problem of non-prehensile manipulation. Assuming that the devil-stick remains confined to the vertical plane, the problem of juggling the stick between two symmetric configurations is considered. Impulsive forces are applied to the stick intermittently and the impulse of the force and its point of application are modeled as control inputs to the system. The dynamics of the devil-stick due to the impulsive forces and gravity is described by half-return maps between two Poincaré sections; the symmetric configurations are fixed points of these sections. A coordinate transformation is used to convert the juggling problem to that of stabilization of one of the fixed points. Inclusion of the coordinate transformation in the dynamic model results in a nonlinear discrete-time system. A dead-beat design for one of the inputs simplifies the control problem and results in a linear time-invariant discrete-time system. Standard control techniques are used to show that symmetric juggling can be achieved from arbitrary initial conditions.

玩弄魔鬼棍棒可谓是不善意操纵的问题。假设魔鬼棒保持在垂直平面内，则考虑了使魔棒在两个对称构型之间跳动的问题。脉冲力间歇地施加到操纵杆，并且该力的脉冲及其施加点被建模为系统的控制输入。魔力棒由于脉冲力和重力的作用通过两个庞加莱部分之间的半回波图来描述。对称配置是这些部分的固定点。使用坐标变换将杂耍问题转换为固定点之一的稳定问题。在动态模型中包含坐标转换会导致非线性离散时间系统。输入之一的无差拍设计简化了控制问题，并导致了线性时不变离散时间系统。使用标准控制技术来表明可以从任意初始条件实现对称杂耍。