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Extra resources for Advances in Dynamics, Instrumentation and Control: Proceedings of the 2006 International Conference (Cdic '06), Queretaro, Mexico, 13 - 16 August 2006
4) and Eq. ( 5 ) into Eq. (6) and likewise Eq. (4) into Eq. (7) yields the two coupled equations of the damped Timoshenko beam motion: + (EIP, ) x + MG(w, )x [MG(wx - P I x -PAW, -wt - P>- PWt =0 (8) = 0. If the damping effects terms are suppressed, the classical set of two coupled PDE developed by Timoshenko arises [ 121 The modelled beam cross-sectional area and density being uniform, the two equations given in (8) can be easily decoupled as follows: K , IP wnttt +EIw, KG KVIW,, -- -PI (10) P21 EIY wXxf+ PO wttt +PAW,, + pvt = 0.
Proof: We present the proof for n even (set n = 2m),being the case when n is odd analogous. +k. Then, F ( t ) is a real polynomial of degree n with all its roots in C+. Consider the polynomial F ( t ) f ( t ) ,which has degree 2n - 1. Notice that po(iw) and f ( i w ) can be written as 24 + p o ( i w )= P ( w 2 ) i w Q ( w 2 ) and + f(h) = p ( w 2 ) iwq(w2), where P, Q , p , and q are real polynomials. We have + F ( i w ) f ( i w )= [ P ( w 2 )- i w Q ( w 2 ) ] [ p ( w 2 ) i w q ( w 2 ) ] = [J'p + w2Qq] + i w ( P q - Q p ) .
I. A singular perturbation analysis of high gain feedback systems. , AC-22, (1977) 931-939. com RAFAEL CASTRO-LINARES' Department of Electrical Engineering, CINVESTAV, Av. I P N No. 2508, Col. net The dynamics modelling of an electrically powered helicopter prototype is presented. The modelling includes the dynamics of the rotor thrust given by a DC electrical motor. Some experimental results are shown for a vertical flight in order to evaluate the model obtained. Keywords: Modelling; Electrically powered helicopters; Helicopter dynamics; Rotor speed control.