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Activities in modifying a structural mathematical model to correlate with its modal test results are summarized. Results from the Viking and Galileo spacecraft, and developments in the parameter estimation of structural mathematical models of large flexible structures using multiple boundary condition tests are presented.
The analysis of the rotational dynamics of the satellite was focused on the rotational amplitude increase of the satellite, with respect to the tether, during retrieval. The dependence of the rotational amplitude upon the tether tension variation to the power 1/4 was thoroughly investigated. The damping of rotational oscillations achievable by reel control was also quantified while an alternative solution that makes use of a lever arm attached with a universal joint to the satellite was proposed. Comparison simulations between the Smithsonian Astrophysical Observatory and the Martin Marietta (MMA) computer code of reteival maneuvers were also carried out. The agreement between the two, completely independent, codes was extremely close, demonstrating the reliability of the models. The slack tether dynamics during reel jams was analytically investigated in order to identify the limits of applicability of the SLACK3 computer code to this particular case. Test runs with SLACK3 were also carried out.
In this paper the authors summarize the activities at the Jet Propulsion Laboratory (JPL) in modifying the structural mathematical model to correlate with its modal test results. In addition to the results from the Viking and Galileo spacecrafts, developments in the parameter estimation of structural mathematical models of large flexible structures using Multiple Boundary Condition Tests (MBCT) are presented.
Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.
The ADAMS computer program for automated analysis of mechanisms and machines is described. The program automatically formulates mathematical models for prototype or existing mechanisms with the minimum necessary physical and geometric data. The model can then be analyzed in various modes of analysis. The outputs (displacements, velocities, acceleration and forces) can be produced in tabular and graphical (plots, wire frame graphics) form. The application of this computer program to simulating satellite docking maneuvers is illustrated.
Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiality are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equation of motion, and then at the level of the equations of motion themselves.
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
The rotational dynamics of irregularly shaped satellites and the origin of Kirkwood Gaps are discussed. The chaotic tumbling of Hyperion and the anomalously low eccentricity of Deimos are examined. The Digital Orrery is used to explore the phase space of the ellipic restricted three body problem near the principal commensurabilities (2/1, 5/2, 3/1, and 3/2). The results for the 3/1 commensurability are in close agreement with those found earlier with the algebraic mapping method. Large chaotic zones are associated with the 3/1, 2/1 and 5/2 resonances, where there are gaps in the distribution of asteroids. The region near the 3/2 resonance, where the Hilda group of asteroids is located, is largely devoid of chaotic behavior. Thus, there is a qualitative agreement between the character of the motion and the distribution of asteroids.
In this paper, the notion of 'near-equivalence in probability' is introduced for identifying a system in the presence of several error sources. Following some basic definitions, necessary and sufficient conditions for the identifiability of parameters are given. The effects of structural error on the parameter estimates for both the deterministic and stochastic cases are considered.
The paper examines the physiology of the cardiovascular system, and to a lesser extent the endocrine, renal, and hematopoietic systems. The paper highlights the aspects of these areas that are most pertinent to space manufacturing, i.e., working in space. Areas covered include the physiological costs of working in microgravity and partial gravity (e.g., the moon or Mars), countermeasures to potentially adverse physiological adaptations, and problems associated with return to earth after long periods of weightlessness.
Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiability are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equations of motion, and then at the level of the equations of motion themselves.
It is shown how systems can be advantageously represented as discrete-event models by using DEVS (discrete-event system specification), a set-theoretic formalism. Such DEVS models provide a basis for the design of event-based logic control. In this control paradigm, the controller expects to receive confirming sensor responses to its control commands within definite time windows determined by its DEVS model of the system under control. The event-based contral paradigm is applied in advanced robotic and intelligent automation, showing how classical process control can be readily interfaced with rule-based symbolic reasoning systems.
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A study of NASA's Systems Management Policy (SMP) concluded that the primary methodology being used by the Mission Operations and Data Systems Directorate and its subordinate, the Networks Division, is very effective. Still some unmet needs were identified. This study involved evaluating methodologies, tools, and techniques with the potential for resolving the previously identified deficiencies. Six preselected methodologies being used by other organizations with similar development problems were studied. The study revealed a wide range of significant differences in structure. Each system had some strengths but none will satisfy all of the needs of the Networks Division. Areas for improvement of the methodology being used by the Networks Division are listed with recommendations for specific action.
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The paper presents a generic statistical model of the (total) modeling error for conventional space structures in their launch configuration. Modeling error is defined as the difference between analytical prediction and experimental measurement. It is represented by the differences between predicted and measured real eigenvalues and eigenvectors. Comparisons are made between pre-test and post-test models. Total modeling error is then subdivided into measurement error, experimental error and 'pure' modeling error, and comparisons made between measurement error and total modeling error. The generic statistical model presented in this paper is based on the first four global (primary structure) modes of four different structures belonging to the generic category of Conventional Space Structures (specifically excluding large truss-type space structures). As such, it may be used to evaluate the uncertainty of predicted mode shapes and frequencies, sinusoidal response, or the transient response of other structures belonging to the same generic category.
The passivity theorem may be used to design robust controllers for structures with positive transfer functions. This result is extended to more general configurations using dissipative system theory. A stability theorem for robust, model-independent controllers of structures which lack collocated rate sensors and actuators is given. The theory is illustrated for non-square systems and systems with displacement sensors.
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