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

Aeroelastic response and limit cycle oscillations for wing-flap-tab section with freeplay in tab

solution of problems in fluid dynamics," Proceedings of Symposia in Applied Mathematics (American Mathematical Society, Providence, Rhode Island, 1963), Vol. 15, pp. 269-288; also Hirt, C. W., "Multidimensional fluid dynamics calculations with high speed computers," AIAA Preprint 65-3 (1965). 15 Freeman, N. C., "Dynamics of a dissociating gas, Part III: Nonequilibrium theory," AGARD Rept. 133 (1957). 16 Marrone, P. V., "Inviscid nonequilibrium flow behind bow and normal shock waves, Part I," Cornell Aeronautical Lab. Rept. QM-1626-A-12 (I) (May 1963).

Generalized aerodynamic forces on an oscillating cylindrical shell -Subsonic and supersonic flow.

Most of real systems are non-linear and they require damage detection. For such non-linear systems, non-linear damage detection methods are necessary for more accurate results. In this paper, a novel non-linear method is introduced using limit cycle oscillations that arise once the bifurcation (flutter) boundary is exceeded and shows greater sensitivity for damage detection versus linear damage detection techniques. Another advantage of this method is that it can be used for health monitoring of linear or non-linear systems. Here a non-linear aeroelastic panel is considered as a model to show the capabilities of the proposed damage detection technique. Also Proper Orthogonal Decomposition (POD) is used to find the number of independent damage locations in the panel. Rayleigh–Ritz method is used to discretizing spatial domain of the system. Damage is modeled as stiffness reduction in the certain region. By comparing Limit Cycle Oscillation of healthy and damaged panel damage level and its location could be obtained with good sensitivity.

Damage detection of an aeroelastic panel using limit cycle oscillation analysis

The aeroelastic stability of rectangular plates in subsonic flow is well documented in literature. For example, the stability of a cantilever plate with a clamped edge parallel to the flow is well understood due to the similarity of this system to an aircraft wing. However, an ongoing push for lighter aerospace structures and novel designs requires advancing the understanding of the aeroelastic stability of plates with nonconventional boundary condition combinations. This paper summarizes the aeroelastic theory and experimental results on the flutter and/or divergence mechanisms of a rectangular plate with different sets of structural boundary conditions. The theory combines a linear plate structural model with a three-dimensional vortex lattice aerodynamic mode to create a high-fidelity frequency domain aeroelastic model. The paper also discusses the development of a modular experimental test bed to test the different boundary conditions. A pair of well-understood boundary condition configurations acts a...

Earl H. Dowell

Papers

Aeroelastic response and limit cycle oscillations for wing-flap-tab section with freeplay in tab

Generalized aerodynamic forces on an oscillating cylindrical shell -Subsonic and supersonic flow.

Damage detection of an aeroelastic panel using limit cycle oscillation analysis

Stability of Rectangular Plates in Subsonic Flow with Various Boundary Conditions

Robust control system design with multiple model approach and its application to active flutter control