We present a mathematical model for analyzing the dynamics of liquid in a spinning container. We also indicate how it can be applied to predict the nutation divergence of a spinning spacecraft without knowing the time...
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We present a mathematical model for analyzing the dynamics of liquid in a spinning container. We also indicate how it can be applied to predict the nutation divergence of a spinning spacecraft without knowing the time constant in advance. The response is determined of an inviscid, incompressible fluid to a prescribed, exponentially growing nutational motion of its container. This use of complex frequencies overcomes the mathematical pathologies associated with standard application of the normal mode concept. Two independent numerical algorithms have been developed for the case of completely full, axisymmetric containers. These perform successfully in different but overlapping parameter regimes, within which excellent agreement is found. Results obtained from the algorithms are presented in the form of pressure at the container boundary and overall torque on the container.
The performance of digital real-time simulations is considered. A figure of merit is derived that quantifies a simulation's fidelity in terms of the time-domain discrepancy between its output and that of the plant...
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The performance of digital real-time simulations is considered. A figure of merit is derived that quantifies a simulation's fidelity in terms of the time-domain discrepancy between its output and that of the plant it simulates, assuming that the plant is linearizable and asymptotically stable. This performance index is then used in deriving an easily automated procedure for calculating optimal values for free parameters in plant discretizations based on a generalized form of open linear multistep integration formulas. The theory is demonstrated in simulating the rigid-body dynamics of a fully articulated helicopter rotor blade system.
A new approach to digital implementation of continuous-scale mathematical morphology is presented. The approach is based on discretization of evolution equations associated with continuous multiscale morphological ope...
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A new approach to digital implementation of continuous-scale mathematical morphology is presented. The approach is based on discretization of evolution equations associated with continuous multiscale morphological operations. Those equations, and their corresponding numerical implementation, can be derived either directly from mathematical morphology definitions or from curve evolution theory. The advantages of the proposed approach over the classical discrete morphology are demonstrated.
An algorithm for shape offsetting is presented that is based on level-set propagation. This algorithm avoids the topological problems encountered in traditional offsetting algorithms, and it deals with curvature singu...
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An algorithm for shape offsetting is presented that is based on level-set propagation. This algorithm avoids the topological problems encountered in traditional offsetting algorithms, and it deals with curvature singularities by including an 'entropy condition' in its numerical implementation.
A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the m...
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A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L2 norms of the modal dynamic residuals vis an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of ''zooming'' on the detected error locations. Several simulation examples which demonstrate the potential of the proposed methodology are discussed.
This paper is concerned with the problem of computing real parameter margins for stabilized, structural dynamic systems with the masses, spring constants, and damping constants as uncertain parameters. numerical algor...
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This paper is concerned with the problem of computing real parameter margins for stabilized, structural dynamic systems with the masses, spring constants, and damping constants as uncertain parameters. numerical algorithms for uncertain systems with multilinear parameters are investigated. It is shown that for a certain class of structural dynamic systems with small passive damping (e.g., flexible structures in space), the computational complexity of the problem can be avoided by modeling the system as a conservative plant, without loss of any practical significance.
This Note has presented a new method to design optimal state-feedback controllers. The resulting closed-loop system has all of its eigenvalues clustered within a region defined by stability and damping requirements. T...
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This Note has presented a new method to design optimal state-feedback controllers. The resulting closed-loop system has all of its eigenvalues clustered within a region defined by stability and damping requirements. The analytical results can be easily extended to include the dynamic output-feedback controller design problem. The major drawback of the present method is the fourfold increases in the computational memory requirements. However, availability of the supercomputer like personal workstations will quickly alleviate this problem in the near future. The focus of current research is on the use of the HVAR-based performance index to achieve robustness against parametric uncertainty.
A control design procedure for disturbance rejection flexible structures with uncertain models was developed based on ideas from traditional multiinput/multioutput quantitative feedback theory. The models can include ...
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A control design procedure for disturbance rejection flexible structures with uncertain models was developed based on ideas from traditional multiinput/multioutput quantitative feedback theory. The models can include uncertainties in both parametric and nonparametric forms. It is shown that computation of quantitative feedback theory bounds can be simplified into an n-step sequential design procedure. At each ith step, the ith element of the diagonal controller is computed from n quadratic inequalities. A 2 x 2 flexible structure example is used to illustrate the technique. (AIAA)
The results of a computational evaluation of several Newton's and quasi-Newton's method solvers are discussed and analyzed. Computer time and memory requirements for iterating a solution to the steady state ar...
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The results of a computational evaluation of several Newton's and quasi-Newton's method solvers are discussed and analyzed. Computer time and memory requirements for iterating a solution to the steady state are recorded for each method. Roe's flux-difference splitting together with the Spekreijse/Van Albada continuous limiter is used for the spatial discretization. Sparse matrix inversions are performed using a modified version of the Boeing real sparse library routines and the conjugate gradient squared algorithm. The methods are applied to exact and approximate Newton's method Jacobian systems for flat plate and flat-plate/wedge-type geometries. Results indicate that the quasi-Newton's method solvers do not exhibit quadratic convergence, but can be more efficient than the exact Newton's method in select cases.
A computational model based on an arbitrary-Lagrangian-Eulerian numerical algorithm is developed for flows separated by a free surface where the surface tension force is important. This model is used to study deformat...
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A computational model based on an arbitrary-Lagrangian-Eulerian numerical algorithm is developed for flows separated by a free surface where the surface tension force is important. This model is used to study deformation and oscillation of cylindrical/spherical droplets with and without external forced convection. The calculated frequency of droplet oscillation agrees well with the analytical value derived from perturbation analysis, and the amplitude of oscillation does not decay with time, which indicates that numerical diffusion and damping do not exist in the adopted algorithm. The deformation of an initially spherical droplet under forced convection is calculated and found consistent with the conclusions in the literature. Good agreement is also obtained in comparison with experimental results for an initially deformed droplet in forced convective flows.
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