This paper assumes a requirement for an unmanned multiunit satellite to be assembled in orbit. The requirement to be met is to bring the satellites together so tha t they do not collide but actually rendezvous. The equations of motion of the rendezvous satellite in a relative coordinate system are derived and used to compute a final injection velocity which would effect collision after a time r. The velocity is corrected periodically by a command guidance system and just before impact retrothrust is applied. A terminal infrared homing sj^stem is required to actually accomplish physical contact and joining of the satellites. The first satellite placed in orbit is the "control satellite" and controls all the satellites to be assembled and contains the ccmputer, command guidance equipment, precision orientation equipment, and other features necessary to effect rendezvous. The succeeding satellites contain a propulsion system, a rough at t i tude control system, and a command receiver plus whatever scientific equipment they carry to perform their basic mission. This paper presents the following:

Terminal Guidance System for Satellite Rendezvous

5. M. Green, J. Schwarz, and E. Witten, Superstring theory, Cambridge Univ. Press, 1987. 6. J. Isenberg, P. Yasskin, and P. Green, Non-self-dual gauge fields, Phys. Lett. 78B (1978), 462-464. 7. B. Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential Geometric Methods in Mathematicas Physics, Lecture Notes in Math., vol. 570, SpringerVerlag, Berlin and New York, 1977. 8. C. LeBrun, Thickenings and gauge fields, Class. Quantum Grav. 3 (1986), 1039-1059. 9. , Thickenings and conformai gravity, preprint, 1989. 10. C. LeBrun and M. Rothstein, Moduli of super Riemann surfaces, Commun. Math. Phys. 117(1988), 159-176. 11. Y. Manin, Critical dimensions of string theories and the dualizing sheaf on the moduli space of (super) curves, Funct. Anal. Appl. 20 (1987), 244-245. 12. R. Penrose and W. Rindler, Spinors and space-time, V.2, spinor and twistor methods in space-time geometry, Cambridge Univ. Press, 1986. 13. R. Ward, On self-dual gauge fields, Phys. Lett. 61A (1977), 81-82. 14. E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. 77NB (1978), 394-398. 15. , Twistor-like transform in ten dimensions, Nucl. Phys. B266 (1986), 245-264. 16. , Physics and geometry, Proc. Internat. Congr. Math., Berkeley, 1986, pp. 267302, Amer. Math. Soc, Providence, R.I., 1987.

Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam)

Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for wh...

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A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

A new method for performing a balanced reduction of a high-order linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshotsisused to obtainlow-rank,reduced-rangeapproximationsto thesystemcontrollability and observability grammiansineitherthetimeorfrequencydomain.Theapproximationsarethenusedtoobtainabalancedreducedorder model. The method is particularly effective when a small number of outputs is of interest. It is demonstrated for a linearized high-order system that models unsteady motion of a two-dimensional airfoil. Computation of the exact grammians would be impractical for such a large system. For this problem, very accurate reducedorder models are obtained that capture the required dynamics with just three states. The new models exhibit far superiorperformancethanthosederived using a conventionalproperorthogonal decomposition. Although further development is necessary, the concept also extends to nonlinear systems.

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Balanced Model Reduction via the Proper Orthogonal Decomposition

On the use of higher-order finite-difference schemes on curvilinear and deforming meshes

This brief paper investigates the optimal selection of online controllers for a linear system with actuator faults in the framework ofH1 control. The occurrence of actuator faults is modeled as a Markov chain to predict future faults. A compatible relationship of H1 controllers is proposed for successive fault modes. In order to shrink the set of all H1 controllers, seven methods are presented to construct a small set of controllers for dierent demands. Then ve selection schemes are proposed to choose a proper controller from a given set of controllers for a given fault mode. Another selection scheme and a pre-selection scheme are presented when there might be false fault detection and identication. Considered together, they provide a powerful solution for all kinds of demands. A motivating example is used to illustrate the proposed methods.

AgeneralH1 faulttolerantcontrolandmanagementfora linearsystemwithactuatorfaults

Reduced-Order Model Analysis For Nanoscale Systems

Rotorcraft have particularly complex and often nonlinear aeroelastic phenomena. This chapters deals with those challenges including ground resonance, air resonance and various forms of aeromechanical instabilities.

Aeroelastic Response of Rotorcraft


 Results from an experimental study on the buckling of a vertically cantilevered plate under corner twisting forces are reported. In this configuration, an interesting and somewhat counter-intuitive behavior is observed in which a laterally loaded slender panel exhibits a subtle instability characterized by nonlinear out-of-plane corner deflections. This is one of the few studies in the literature that investigates the buckling of cantilevered plates and appears to be the only experimental study of buckling under twisting loads, i.e., loading the plate with point loads at the free corners and in opposite directions. This paper discusses the practical aspects of experimental verification and methodology and evaluates the effect of the plate aspect ratio (AR) on the non-dimensional buckling load in this configuration. In addition, experimental results are compared to finite element analysis (FEA) simulations performed on accessible software. There is generally good agreement between the experiment and the finite element simulation for the change of buckling load with plate aspect ratio. The non-dimensional buckling load appears to decrease asymptotically with increasing aspect ratio, though the correlation of experiment and computation is less consistent as aspect ratio increases due to experimental and computational limitations.

Buckling of a vertically mounted cantilevered plate under static torsional corner loads – experiment and theory

The general relations for the problem of interaction of a permeable shell with a fluid flow are considered. They may be used to determine both the forms (shapes) and stress state of perforated shells and plates, parachute, networks (nets), etc., as well as the pressure and velocity field in the flow around them.

Earl H. Dowell

Papers

AgeneralH1 faulttolerantcontrolandmanagementfora linearsystemwithactuatorfaults

Reduced-Order Model Analysis For Nanoscale Systems

Aeroelastic Response of Rotorcraft

Buckling of a vertically mounted cantilevered plate under static torsional corner loads – experiment and theory

Interaction of a Permeable Shell with a Fluid Flow