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

Evolution of Airplanes, and What Price Speed?

An experimental program has been carried out to investigate a class of flows which is of interest with regard to the aeroelastic flutter of flexible cylinders. The flowfield of interest is the swirling flow between two concentric cylinders, of which the inner one is stationary and the outer one rotates. Air is admitted into the annulus between the cylinders through inlets in the wall of the rotating outer cylinder near one end of the apparatus and is exhausted through an annular outlet surrounding the inner cylinder near the other end. Measurements of the resulting flowfield have been made for a wide range of flow rates, outer cylinder rotational speeds, and inlet geometries. Approximate scaling laws for the velocity field have been developed, and dimensionless parameters have been defined which correlate the effects of the various inlet conditions which were tested. Nomenclature Aan = cross-sectional area of annulus A„ = total cross-sectional area of inlets d = internal diameter of inlet tubes / = inner cylinder structural frequency I = length of inlet tubes m =mass flow, Ibm/sec M = dimensionless momentum flux quantity, Eq. (4) N = number of inlets p,pt = static pressure, pitot pressure r = radius from cylinder axis Rj = radius of inner cylinder (outside) R0 = radius of outer cylinder (inside) R = dimensionless radius = (r-Rt)/(R0 —/?/) t = dimensionless "residence time" quantity, Eq. (5) Um = average axial velocity in the annulus =m/pAan V = magnitude of fluid velocity Vn = average radial velocity in inlets =m/pAn Vt = tangential component of fluid velocity Vz = axial component of fluid velocity z = axial coordinate 0 = yaw angle A = pitot pressure referenced to the static pressure at the inner cylinder =prp(Ri) T =Vtr, circulation T0 =uR20, (ideal) circulation at outer cylinder oj = angular velocity of outer cylinder

Swirling Flows between Coaxial Cylinders with Injection by Radial Jets

Fluttering isotropic rectangular flat plate fatigue life estimation, taking into account stress, dynamic pressure, frequency, Mach number and plate thickness

Fatigue life estimation of fluttering panels

Presented is a discrete adjoint approach for computing nonlinear unsteady aeroelastic geometric design sensitivities, which can subsequently be used for nonlinear unsteady aeroelastic geometric des...

Earl H. Dowell

Papers

Evolution of Airplanes, and What Price Speed?

Swirling Flows between Coaxial Cylinders with Injection by Radial Jets

Fatigue life estimation of fluttering panels

Discrete Adjoint Approach for Nonlinear Unsteady Aeroelastic Design Optimization

An assessment and extension of geometrically nonlinear beam theories