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...

/pdf/a-survey-of-projection-based-model-reduction-methods-for-3yjqbxk305.pdf

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.

/pdf/balanced-model-reduction-via-the-proper-orthogonal-5c77iwc45j.pdf

Balanced Model Reduction via the Proper Orthogonal Decomposition

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

A thin elastic shell under tension is wrapped around a rigid curved surface; the latter renders the stiffness of the shell effectively nonlinear. The static aeroelastic stability of the shell is examined for a subsonic flow along the axis of the shell and the longitudinal axis of the curved rigid surface. The minimum flow velocity for which the elastic shell will deform statistically is determined, as well as the amplitude of the deformation as a function of flow velocity

Static subsonic aeroelastic stability of a shell wrapped around a rigid surface

An equivalent linear viscous damping formula for beams with rather general dry friction support conditions is proposed. The effect of normal force support reaction at the dry friction support on response is also discussed. Comparisons of experimental results to those obtained from an approximate solution and numerical time integration are made. Generally good agreement is found among the several results.

Damping in beams with multiple dry friction supports

A linear time-invariant optimal estimator for uncertain output matrix systems is considered. Uncertainty of the output matrix is represented by a set of multiple parameters, and the optimal estimator is introduced by minimizing the expected cost function of the estimation error. When the number of measured variables is small, the order of the optimal estimator does not depend on the number of models, and meeting the computational demand becomes quite feasible. >

An estimator for uncertain output matrix systems

Presented are flutter-onset trends of the F-16 fighter computed using a harmonic balance version of the NASA OVERFLOW 2 flow solver code. The harmonic technique enables one to model unsteady aerodynamics and aeroelastic response in the frequency domain with reduced computational cost compared to time marching solutions. Computed results compare well to flutter results computed using a separate harmonic balance computational flow solver code developed at Duke University. Select aeroelastic limit cycle oscillation results are also presented.

http://enu.kz/repository/2010/AIAA-2010-2632.pdf

F-16 Fighter Aeroelastic Computations Using a Harmonic Balance Implementation of the OVERFLOW 2 Flow Solver

The aeroelastic stability is examined of an infinitely long panel of finite width enclosed in a duct such that both the upper and lower surfaces of the panel are exposed to an inviscid, and compressible flow. The panel behavior is accounted for by small deflection plate theory, whereas the aerodynamic forces acting on the panel are described by the classical linearized small disturbance potential theory. As such, a self-consistent theoretical model is constructed for the asymptotic behavior of the panel. Two panel boundary conditions are considered; the panel is assumed to be either simply supported, or clamped along the side edges. For the simply supported case, rather extensive numerical results have been obtained. The effects of Mach number, air/panel mass ratio, and duct dimension on the flutter velocity are determined. a a* b c CQ c* D E h h* hp L / /* M m P t U U* U*T W x y z y Nomenclature speed of sound a/c0 panel width wave speed reference wave speed, 2n(D/pmhb2)1/2 C/CQ plate stiffness modulus of elasticity height of duct nondimensional height of duct, h/b panel thickness panel length wavelength nondimensional wavelength, l/b Mach number, U*/a* number of modes pressure time flow velocity U/CQ critical flutter velocity panel deflection streamwise coordinate spanwise coordinate coordinate perpendicular to plane of panel separation constant nondimensional dynamic pressure, /x£/*2

Earl H. Dowell

Papers

Static subsonic aeroelastic stability of a shell wrapped around a rigid surface

Damping in beams with multiple dry friction supports

An estimator for uncertain output matrix systems

F-16 Fighter Aeroelastic Computations Using a Harmonic Balance Implementation of the OVERFLOW 2 Flow Solver

Flutter of an infinitely long panel in a duct