An approach to dynamics and control of flexible systems

Abstract

This paper presents a rather general r~cursive formulation of flexible niultibody sys ten~s It accormts for an arbitrary level of branching, character of the structural members, orbital perturbations, etc , and introducing a concept of equivalent disconnected system, it easily leads to an efficient order 11 algorithm A numerical simulation code based upon the formulation has been developed, which showed high accln-acy in terms of sys ten~ energy and ang~dar moment~un conse rva t io~~ Versatility of tllc approach is illr~stratcd t h o u g h paran~etric studies of several particular sysvectors ( column mahices ) matrix which is equivalent to the vector product operatio11 E x ; Eq.( l4) a E matrix of elements where Si, b are vectors. a b value of n a t b 0 f o r c ~ w.r t 1,lw i~tertial frame inboard body nunlhw of body 1 set of body nu~r~bcr s o~~t,boart l to botly T set of level I body n u ~ r ~ b e r s mass generalized coordinate vect,or ~lonholono~nic velocity vect,or velocity vector after constraint relative velocity vector of body i w.r.t. the body ii, fixed frame; Eq.(12) velocit,y vrctor for tlte rq~~ iva . I~ ,~ l l discotnlected sys te~n; 15q.(34) position vector to a Itlass cdcmr~lt w.r.L. tllc illertial framc position vector to the ~lorniml ccnt.c\r of rnass w.r.t. the inertial frame Graduate student, University of Tokyo t Professor t Piofessor, Fellow AIAA Copyright 0 1 9 9 4 by the Amet-ican lnstitrttr of nlat,ricf,s transpose unit ~na t r ix forces other than the generalized force; Eq ( 7 ~ ) total force; Eq.(7d) total force after cor~straint; Eq.(lOb) n ~ a x i n ~ u ~ n bra ch level mass matrix; Eq. (7a) mass matrix aft,er constraint,; Eq (IOa) mass matrix of the equivalent discon~ t ( ~ t , c t i sys t e~n ; Eqs.(36) arid (37) nrmthrr of bodies ge~leralizcd force; Eq (7b)