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Method is modification of generalized Newton-Ralphson algorithm for analyzing two-point boundary problems. It constructs sequence of solutions that converge to precise dynamic solution in the sequence limit. Program calculates periodic orbits in either circular or elliptical restricted three-body problems.
Mathematical models for calculating flexible swash-plate effects on vibratory and mechanical stability characteristics of helicopter rotor systems
The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.
A test/analysis correlation criterion for the analytical model accuracy requirement has been developed. It is based on the principle of equal errors from the model inaccuracy and the uncertainties of dynamic environments. The forcing functions are idealized to establish the base for uncertainty definition and the maximum allowable errors from these uncertainties are obtained. Then the model accuracy requirement is established by comparing the responses due to the model errors to those due to the forcing function uncertainties.
Program has been developed that analytically determines effects of nonuniform swash-plate support stiffness, swash-plate flexibility, and out-of-blade track on vibratory mechanical stability characteristics of helicopter rotor systems. Analysis is based on combined Laplace transform and associated matrix approach.
The objective is to present the activities at TRW in developing the capability to simulate the behavior of large flexible multibody space structures. The features of the simulation tools are: (1) to accommodate all rigid/flexible body degrees-of-freedom which incorporate the control system models and external forces, (2) to provide the flexibility to incorporate engineering-defined models and to retain parameters of significance to the engineer, (3) to reduce the computation cost by one order of magnitude (two orders of magnitude compared to a CRAY 1S), and (4) to keep it versatile so that radical variations in anticipated space structures can be accommodated. The current computer tools to simulate multibody systems appear not only to be very costly and time consuming, but also do not produce the desired fidelity of the mathematical models. In summary, a multibody simulation tool will be developed in the near future which will allow solution of the dynamics and controls of the deployment of the LDR backup structure, or the problem associated with the robotic assembly of the structure. The tools will allow the engineer to define the modeling technique and solve problems in less time and at reduced cost.
A joint effort was undertaken on a Precision Segmented Reflector (PSR) Project. The missions in which the PSR is to be used will use large (up to 20 m in diameter) telescopes. The essential requirement for the telescopes is that the reflector surface of the primary mirror must be made extremely precise to allow no more than a few microns of errors and, additionally, this high surface precision must be maintained when the telescope is subjected to on-orbital mechanical and thermal disturbances. Based on the mass, size, and stability considerations, reflector surface formed by segmented, probably actively or passively controlled, composite panels are regarded as most suitable for future space based astronomical telescope applications. In addition to the design and fabrication of composite panels with a surface error of less than 3 microns RMS, PSR also develops related reflector structures, materials, control, and sensing technologies. As part of the planning effort for PSR Technology Demonstration, a system model which couples the reflector, consisting of panels, support truss and actuators, and the optical bench was assembled for dynamic simulations. Random vibration analyses using seismic data obtained from actual measurements at the test site designated for PSR Technology Demonstration are described.
Increasing demands on the fidelity of simulations for real-time and high-fidelity simulations are stressing the capacity of modern processors. New integration techniques are required that provide maximum efficiency for systems that are parallelizable. However many current techniques make assumptions that are at odds with non-cascadable systems. A new serial multi-step/multi-rate integration algorithm for dual-timescale continuous state systems is presented which applies to these systems, and is extended to a parallel multi-step/multi-rate algorithm. The superior performance of both algorithms is demonstrated through a representative example.
This paper presents a set of studies in full mission simulation and the development of a predictive computational model of human performance in control of complex airspace operations. NASA and the FAA have initiated programs of research and development to provide flight crew, airline operations and air traffic managers with automation aids to increase capacity in en route and terminal area to support the goals of safe, flexible, predictable and efficient operations. In support of these developments, we present a computational model to aid design that includes representation of multiple cognitive agents (both human operators and intelligent aiding systems). The demands of air traffic management require representation of many intelligent agents sharing world-models, coordinating action/intention, and scheduling goals and actions in a potentially unpredictable world of operations. The operator-model structure includes attention functions, action priority, and situation assessment. The cognitive model has been expanded to include working memory operations including retrieval from long-term store, and interference. The operator's activity structures have been developed to provide for anticipation (knowledge of the intention and action of remote operators), and to respond to failures of the system and other operators in the system in situation-specific paradigms. System stability and operator actions can be predicted by using the model. The model's predictive accuracy was verified using the full-mission simulation data of commercial flight deck operations with advanced air traffic management techniques.
The Dynamics Explorer (DE) program summarizes its accomplishments during the first 5 years since the launch of the two DE satellites. This introduction to six review articles provides background information and a brief history of the program, especially citing the contributions of many people to its development. The principal investigators who had primary responsibility to implement the program are listed, together with the instruments they provided. Orbital information and approaches and constraints to data acquisition are explained. The brief description of the ground data processing and analysis system provides information on access to data catalogs and data sets. Each review article is then placed in the context of the categories of scientific objectives of the program.
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Linear fractional transformation for obtaining rational approximations to response of physical system defined by second order nonlinear differential equation with constant coefficients
Asymptotic and periodic behavior prediction for nonlinear control system with mathematical model of rigid body vehicle
Orbital motion in restricted three-body problem
Game theory for optimal parameter control of payload delivery by limited thrust engine space flight
Stochastic Liapunov functions and invariant set concept
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Invariance method for extending Liapunov function to distributed parameter system