Based on (w,z) parameter attitude stability control of axisymmetric 3D pendulum

This paper studies attitude control problem of axisymmetric 3D pendulum based on (w,z). 3D rigid pendulum (that is, put three-dimensional rotation) composed by a frictionless rigid body of fixed-point supported. When axisymmetric case, the symmetry axis is the inertia axis for the rigid body, the 3D rigid pendulum is axisymmetric 3D pendulum. According to its center of mass and friction-free fulcrum fixed relative position, axisymmetric 3D pendulum can be divided into two cases: one is the center of mass below the pivot, that is hanging posture; the other is the center of mass above the pivot, that is the inverted posture. As the Euler angle existed singularity problems, a new attitude described method was introducted, that is (w,z) parameter description. And argued the attitude kinematics equation of axisymmetric 3D pendulum, given the direction cosine matrix by the (w,z) parameters described in. At the same time the use of (w,z) parameters, design a new control law makes the axisymmetric 3D rigid body placed in its inverted position asymptotically stable. Simulation results also verify the control method effect for axisymmetric 3D pendulum.