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DESIGN OF CONTROL LAWS
Exact Computation of the Response Envelope
APPENDIX A METRIC PROPERTIES OF THE FUNCTION
Admissible forcing functions admissible initial conditions angular momentum exchange assumed asymptotically stable attitude control systems attitude error feedback body angular velocity body coordinates boundary comparison model components Consider constant angular velocity control moment gyros corresponding cross product curve defined by equation denoted dynamic equation eigenvector envelope is given equation l6 equivalence error angle error function external torque Figure George Meyer given system global analysis grid G gyroscopic coupling Hamilton-Jacobi equation Hence inertial space initial conditions 6o inner gimbal angles kinematic equation Liapunov functions magnitude function magnitude of attitude maximum nominal control law optimal control outlined in table parameters possible control situations possible motions procedure properties of three-dimensional reaction wheels response envelope rotation matrix saturation sensors set of admissible simulation skew-symmetric matrix spacecraft attitude spherical errors spherically bounded spherically symmetric model star trackers Suppose target angular velocity target attitude motion three-dimensional rotations total angular momentum trajectory unit vector upper estimate