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An unconventional approach is considered to a computer-aided analysis of the dynamics of large systems. The proposed approach is based on the use of symbolic computing methods that are applied directly to the system equations. Other areas of application of this symbolic method are also pointed out.
We report the discovery and dynamical analysis of 2015 BP$_{519}$, an extreme Trans-Neptunian Object detected detected by the Dark Energy Survey at a heliocentric distance of 55 AU and absolute magnitude Hr= 4.3. The current orbit, determined from a 1110-day observational arc, has semi-major axis $a\approx$ 450 AU, eccentricity $e\approx$ 0.92 and inclination $i\approx$ 54 degrees. With these orbital elements, 2015 BP$_{519}$ is the most extreme TNO discovered to date, as quantified by the reduced Kozai action, which is is a conserved quantity at fixed semi-major axis $a$ for axisymmetric perturbations. We discuss the orbital stability and evolution of this object in the context of the known Solar System, and find that 2015 BP$_{519}$ displays rich dynamical behavior, including rapid diffusion in semi-major axis and more constrained variations in eccentricity and inclination. We also consider the long term orbital stability and evolutionary behavior within the context of the Planet Nine Hypothesis, and find that BP$_{519}$ adds to the circumstantial evidence for the existence of this proposed new member of the Solar System, as it would represent the first member of the population of high-i, $\varpi$-shepherded TNOs.
Apollo lunar module structural integrity for lunar landing verified by Monte Carlo dynamic analysis
Computerized step-jump and time-transient dynamic analysis application to gimbal mounted Rayleigh- step gas-lubricated thrust bearing design
This report summarizes the major activities and accomplishments carried out by the Flight Dynamics Analysis Branch (FDAB), Code 595, in support of flight projects and technology development initiatives in Fiscal Year (FY) 2004. The report is intended to serve as a summary of the type of support carried out by the FDAB, as well as a concise reference of key accomplishments and mission experience derived from the various mission support roles. The primary focus of the FDAB is to provide expertise in the disciplines of flight dynamics including spacecraft navigation (autonomous and ground based); spacecraft trajectory design and maneuver planning; attitude analysis; attitude determination and sensor calibration; and attitude control subsystem (ACS) analysis and design. The FDAB currently provides support for missions and technology development projects involving NASA, other government agencies, academia, and private industry.
This report summarizes the major activities and accomplishments carried out by the Flight Dynamics Analysis Branch (FDAB), Code 595, in support of flight projects and technology development initiatives in Fiscal Year (FY) 2005. The report is intended to serve as a summary of the type of support carried out by the FDAB, as well as a concise reference of key accomplishments and mission experience derived from the various mission support roles. The primary focus of the FDAB is to provide expertise in the disciplines of flight dynamics including spacecraft navigation (autonomous and ground based), spacecraft trajectory design and maneuver planning, attitude analysis, attitude determination and sensor calibration, and attitude control subsystem (ACS) analysis and design. The FDAB currently provides support for missions and technology development projects involving NASA, other government agencies, academia, and private industry.
This viewgraph report presents an overview of activities and accomplishments of NASA's Marshall Space Flight Center's Applied Fluid Dynamics Analysis Group. Expertise in this group focuses on high-fidelity fluids design and analysis with application to space shuttle propulsion and next generation launch technologies. Topics covered include: computational fluid dynamics research and goals, turbomachinery research and activities, nozzle research and activities, combustion devices, engine systems, MDA development and CFD process improvements.
This paper concerns the transient dynamic analysis of the B-52 aircraft carrying the Space Shuttle solid-rocket booster drop-test vehicle (SRB/DTV). The NASA structural analysis (NASTRAN) finite-element computer program was used in the analysis. The B-52 operating conditions considered for analysis were (1) landing and (2) braking on aborted takeoff runs. The transient loads for the B-52 pylon front and rear hooks were calculated. The results can be used to establish the safe maneuver envelopes for the B-52 carrying the SRB/DTV in landings and brakings.
In this paper an automated algorithmic method is presented for the dynamic analysis of geared trains/transmissions. These are treated as a system of interconnected flexible bodies. The procedure developed explains the switching of constraints with time as a result of the change in the contacting areas at the gear teeth. The elastic behavior of the system is studied through the employment of three-dimensional isoparametric elements having six degrees-of-freedom at each node. The contact between the bodies is assumed at the various nodes, which could be either a line or a plane. The kinematical expressions, together with the equations of motion using Kane's method, strain energy concepts, are presented in a matrix form suitable for computer implementation. The constraint Jacobian matrices are generated automatically based on the contact information between the bodies. The concepts of the relative velocity at the contacting points at the tooth pairs and the subsequent use of the transmission ratios in the analysis is presented.
The multiple mesh/single stage dynamics program is a gear tooth analysis program which determines detailed geometry, dynamic loads, stresses, and surface damage factors. The program can analyze a variety of both epicyclic and single mesh systems with spur or helical gear teeth including internal, external, and buttress tooth forms. The modifications refine the options for the flexible carrier and flexible ring gear rim and adds three options: a floating Sun gear option; a natural frequency option; and a finite element compliance formulation for helical gear teeth. The option for a floating Sun incorporates two additional degrees of freedom at the Sun center. The natural frequency option evaluates the frequencies of planetary, star, or differential systems as well as the effect of additional springs at the Sun center and those due to a flexible carrier and/or ring gear rim. The helical tooth pair finite element calculated compliance is obtained from an automated element breakup of the helical teeth and then is used with the basic gear dynamic solution and stress postprocessing routines. The flexible carrier or ring gear rim option for planetary and star spur gear systems allows the output torque per carrier and ring gear rim segment to vary based on the dynamic response of the entire system, while the total output torque remains constant.
This paper has two objectives. The first objective is to formulate a 3-dimensional Finite Element Model for the dynamic analysis of helicopter rotor blades. The second objective is to implement and analyze a dual-primal iterative substructuring based Krylov solver, that is parallel and scalable, for the solution of the 3-D FEM analysis. The numerical and parallel scalability of the solver is studied using two prototype problems - one for ideal hover (symmetric) and one for a transient forward flight (non-symmetric) - both carried out on up to 48 processors. In both hover and forward flight conditions, a perfect linear speed-up is observed, for a given problem size, up to the point of substructure optimality. Substructure optimality and the linear parallel speed-up range are both shown to depend on the problem size as well as on the selection of the coarse problem. With a larger problem size, linear speed-up is restored up to the new substructure optimality. The solver also scales with problem size - even though this conclusion is premature given the small prototype grids considered in this study.
The complexities of turbine engine blade vibration are compounded by blade geometry, temperature gradients, and rotational speeds. Experience indicates that dynamics analysis using the finite element approach provides an effective means for predicting vibration characteristics of compressor and turbine blades whose geometry may be irregular, have curved boundaries, and be subjected to high temperatures and speeds. The NASTRAN program was chosen to help analyze the dynamics of normal modes, rotational stiffening and thermal effects on the normal modes, and forced responses. The program has produced reasonable success. This paper presents the analytical procedures and the NASTRAN results, in comparison with a conventional beam element program and laboratory data.
Analytical procedures and digital computer code are presented for the dynamic analysis of a flexible spacecraft with rotating components. Topics, considered include: (1) nonlinear response in the time domain, and (2) linear response in the frequency domain. The spacecraft is assumed to consist of an assembly of connected rigid or flexible subassemblies. The total system is not restricted to a topological connection arrangement and may be acting under the influence of passive or active control systems and external environments. The analytics and associated digital code provide the user with the capability to establish spacecraft system nonlinear total response for specified initial conditions, linear perturbation response about a calculated or specified nominal motion, general frequency response and graphical display, and spacecraft system stability analysis.
The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described.
A rigorous theory and corresponding computational algorithms was developed for a variety of problems regarding the analysis of composite beams and plates. The modeling approach is intended to be applicable to both static and dynamic analysis of generally anisotropic, nonhomogeneous beams and plates. Development of a theory for analysis of the local deformation of plates was the major focus. Some work was performed on global deformation of beams. Because of the strong parallel between beams and plates, the two were treated together as thin bodies, especially in cases where it will clarify the meaning of certain terminology and the motivation behind certain mathematical operations.
Several criteria that may be used to evaluate the merits of some of the existing techniques for the dynamic analysis of large structures which involve division into substructures or components are examined. These techniques make use of component displacement modes to synthetize global systems of generalized coordinates and, for that reason, they have come to be known as modal synthesis or component mode methods. Two techniques have been found to be particularly useful - i.e., the modal synthesis method with fixed attachment modes, and the modal synthesis method with free attachment modes. These two methods are treated in detail, and general flow charts are presented for guidance in computer programming.
The use of an orthogonal set of specially selected Ritz vectors is shown to be very effective in reducing the cost of dynamic analysis by modal superposition. Several mechanical structures are examined, and the Ritz vector approach is compared to the classical eigenvector approach on the basis of cost, accuracy and elapsed analysis (throughput) time. Mathematical proof of the completeness of orthogonal Ritz vectors is provided for the case of a positive definite mass matrix and a symmetric stiffness matrix.
This presentation discusses Spectral Proper Orthogonal Decomposition (SPOD) of Unsteady Pressure-Sensitive Paint (uPSP) measurements in the Space Launch System (SLS) Ascent Transient Aerodynamics Test (ATAT) and its application in the structural dynamics analysis.