Dynamics of Rigid Rotor mounted on Flexible Supports

(C) 2003 - Roberto Lot

> restart:

> mylib :="C:\LIBS": libname := mylib,libname: with(MBsymba):

[Maple Metafile]

1st define th body frame

> alpha(t), beta(t), rotations due to bearings elastiticy

> Omega; constant spin velocity

> BF := rotate('Y',alpha(t)) * rotate ('X',beta(t)) * rotate('Z',Omega*t);

alpha(t), beta(t), Omega

BF := matrix([[cos(alpha(t))*cos(Omega*t)+sin(alpha...

we assume that rotations due to elasticity are smalls

> sm_vars := {alpha(t),beta(t)};
BF := linearize(BF,sm_vars,t);

sm_vars := {alpha(t), beta(t)}

BF := matrix([[cos(Omega*t), -sin(Omega*t), alpha(t...

definition of rotor mass properties

> rotor := make_BODY(BF, m, It,It,Ia): show(%);

BODY(inertia = matrix([[It, 0, 0], [0, It, 0], [0, ...

> k, linear stiffness of the bearing

> L; distance between beerigns

> MX := -k*(L/2)^2*alpha(t); elastic torque

> MY := -k*(L/2)^2*beta(t); elastic torque

k, L

MX := -1/4*k*L^2*alpha(t)

MY := -1/4*k*L^2*beta(t)

reative torque due to the bearings

> elastic_bearings := make_TORQUE(ground, MX,MY,0, rotor): show(%);

TORQUE(comps = matrix([[-1/4*k*L^2*alpha(t)], [-1/4...

> eqns := euler_equations({rotor,elastic_bearings},CoM(rotor),ground):
eqns := linearize(eqns,sm_vars,t):
show(%);

VECTOR(comps = matrix([[diff(alpha(t),t)*Ia*Omega+1...