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EQUATIONS OF MOTION OF CONTROLLED FLEXIBLE VEHICLES
B Use of a Rate Network
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actuators Appendix attitude control balanced control forces center of mass centroidal line Chapter characteristic equation characteristic roots computer solutions consider control axes control moments control system coordinates Coriolis forces damping ratio defined by Eq deflection derived determined equations of motion excited flexible mode flexible vehicles employing flexural modes flexural motions force and sensor forces or moments formulas higher modes indicated inertia inertial space linear loci LOCUS FOR UNCOUPLED marginal stability modal poles modal roots mode number mode shapes natural frequency observe from Eqs obtain orthogonal parameters points of control Poisson's ratio rate network rigid mode rigid-body motion rigid-mode root locus rotating sensor locations shown in Fig small gains small vector angle spin axis spin speed spinning space station stable region Substituting Eqs symmetric cross section third mode tion toroid transfer function UNCOUPLED SYSTEM undeflected values xx yy xy yields yy xy yx zero