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EQUATIONS OF MOTION OF CONTROLLED FLEXIBLE VEHICLES ll
F Roots for Large Gains
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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 coupling 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 imaginary indicated inertia inertial space linear loci LOCUS FOR UNCOUPLED marginal stability modal poles modal roots mode number mode shapes n"-mode natural frequency nth mode 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 spin axis spin speed spinning space station stable region Substituting Eqs symmetric cross section third mode tion toroid transfer function uncoupled system undeflected values velocity yields