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Results for “Applied Dynamical Systems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

The transfer function method for gear system dynamics applied to conventional and minimum excitation gearing designs

A transfer function method for predicting the dynamic responses of gear systems with more than one gear mesh is developed and applied to the NASA Lewis four-square gear fatigue test apparatus. Methods for computing bearing-support force spectra and temporal histories of the total force transmitted by a gear mesh, the force transmitted by a single pair of teeth, and the maximum root stress in a single tooth are developed. Dynamic effects arising from other gear meshes in the system are included. A profile modification design method to minimize the vibration excitation arising from a pair of meshing gears is reviewed and extended. Families of tooth loading functions required for such designs are developed and examined for potential excitation of individual tooth vibrations. The profile modification design method is applied to a pair of test gears.

Mark, W. D.↗
NASA NTRS1982

Application of control theory to dynamic systems simulation

The application of control theory is applied to dynamic systems simulation. Theory and methodology applicable to controlled ecological life support systems are considered. Spatial effects on system stability, design of control systems with uncertain parameters, and an interactive computing language (PARASOL-II) designed for dynamic system simulation, report quality graphics, data acquisition, and simple real time control are discussed.

Auslander, D. M.↗
NASA NTRS1989

The use of real-time, hardware-in-the-loop simulation in the design and development of the new Hughes HS601 spacecraft attitude control system

Realtime simulation and hardware-in-the-loop testing is being used extensively in all phases of the design, development, and testing of the attitude control system (ACS) for the new Hughes HS601 satellite bus. Realtime, hardware-in-the-loop simulation, integrated with traditional analysis and pure simulation activities is shown to provide a highly efficient and productive overall development program. Implementation of high fidelity simulations of the satellite dynamics and control system algorithms, capable of real-time execution (using applied Dynamics International's System 100), provides a tool which is capable of being integrated with the critical flight microprocessor to create a mixed simulation test (MST). The MST creates a highly accurate, detailed simulated on-orbit test environment, capable of open and closed loop ACS testing, in which the ACS design can be validated. The MST is shown to provide a valuable extension of traditional test methods. A description of the MST configuration is presented, including the spacecraft dynamics simulation model, sensor and actuator emulators, and the test support system. Overall system performance parameters are presented. MST applications are discussed; supporting ACS design, developing on-orbit system performance predictions, flight software development and qualification testing (augmenting the traditional software-based testing), mission planning, and a cost-effective subsystem-level acceptance test. The MST is shown to provide an ideal tool in which the ACS designer can fly the spacecraft on the ground.

Slafer, Loren I.↗
DOE OSTI2025

Construction of approximate invariants for nonintegrable Hamiltonian systems

We present a method to construct high-order polynomial approximate invariants (AI) for nonintegrable Hamiltonian dynamical systems and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps expressed as square matrices, AIs can be constructed order by order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Construction of approximate invariants for non-integrable Hamiltonian systems

We present a method to construct high-order polynomial approximate invariants (AI) for non integrable Hamiltonian dynamical systems, and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Applied Dynamical Systems↗
NASA NTRS1994

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗
DOE OSTI2025

Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

Applied Dynamical Systems↗
NASA NTRS1988

A knowledge-based approach to identification and adaptation in dynamical systems control

Artificial intelligence techniques are applied to the problems of model form and parameter identification of large-scale dynamic systems. The object-oriented knowledge representation is discussed in the context of causal modeling and qualitative reasoning. Structured sets of rules are used for implementing qualitative component simulations, for catching qualitative discrepancies and quantitative bound violations, and for making reconfiguration and control decisions that affect the physical system. These decisions are executed by backward-chaining through a knowledge base of control action tasks. This approach was implemented for two examples: a triple quadrupole mass spectrometer and a two-phase thermal testbed. Results of tests with both of these systems demonstrate that the software replicates some or most of the functionality of a human operator, thereby reducing the need for a human-in-the-loop in the lower levels of control of these complex systems.

Glass, B. J.↗
NASA NTRS1990

Discretization chaos - Feedback control and transition to chaos

Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.

Grantham, Walter J.↗
NASA NTRS1992

Computation of magnetic suspension of maglev systems using dynamic circuit theory

Dynamic circuit theory is applied to several magnetic suspensions associated with maglev systems. These suspension systems are the loop-shaped coil guideway, the figure-eight-shaped null-flux coil guideway, and the continuous sheet guideway. Mathematical models, which can be used for the development of computer codes, are provided for each of these suspension systems. The differences and similarities of the models in using dynamic circuit theory are discussed in the paper. The paper emphasizes the transient and dynamic analysis and computer simulation of maglev systems. In general, the method discussed here can be applied to many electrodynamic suspension system design concepts. It is also suited for the computation of the performance of maglev propulsion systems. Numerical examples are presented in the paper.

He, J. L.↗