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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)

This paper voposes a control law that stabilizes momentum transfer maneuver using multi-wheels, which is proved here analytically via Liapunov's direct method. As another consequence, this paper point out equilibrium "singular states" which closed momentum transfer control may fall into, and from which any evasive path cannot be found. Sufficient conditions are provided here so that such singular states can be circumvented by appropriate control law proposed here. It is revealed that six singular points including trivial target state exist in general. It is also shown that appropriate choice of control law reduces number of "singular states." As a practical application, numerical examples are shown as to scientific X-ray telescope satellite ASTRO-D, which is scheduled to be launched in February, 1993 by ISAS (Institute of Space and Astronautical Science). Numerical analysis concludes singular states other than desired fmal target are all unstable and unreachable as for ASTRO-D and proves momentum transfer control law proposed here uniquely determines final state as well as wheels spin rates.

r A new design method o f insensit ive control lers is presented. Th is method, termed 1d.C.V. ( Maximum Cost Variation ), belongs to the G.C.C. ( Guaranteed Cost Control ) and it realizes both the robust stabi l i ty and the preservation o f cost th rough the expl ic i t solution o f insensi t iv i ty i n L.Q. form. Af te r comparative studies w i th other methods, three numerical examples are given to show i t s effectiveness to fhe design o f insensit ive control lers.