Search NASA⌕ Search

SEARCH · Search NASA

Results for “time of initial motion”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Optimal Electrodynamic Tether Phasing Maneuvers

We study the minimum-time orbit phasing maneuver problem for a constant-current electrodynamic tether (EDT). The EDT is assumed to be a point mass and the electromagnetic forces acting on the tether are always perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to compare similar trajectories for a constant thrust phasing maneuver and we find that the time of flight is longer for the constant thrust case with similar initial thrust values and phase angles. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations.

Bitzer, Matthew S.↗
NASA NTRS1979

The growth of aspherical structure in the universe - Is the Local Supercluster an unusual system

The growth and subsequent collapse of homogeneous ellipsoidal perturbations in a uniform expanding background is considered as a simple model for the formation of large-scale aspherical structures in the observed universe. Numerical calculations of the evolution of such perturbations turn out to be well described by an approximate analytic solution of the equations of motion, and simple relationships are found between the initial shape of a perturbation and its shape and kinematic properties at the time of collapse. Perturbations do not change their shape significantly until they reach a density contrast of order unity. As a result, structures with the kinematic properties of the Local Supercluster should form much more commonly in a low-density universe than in a flat universe. The homogeneity of the local Hubble flow, the motion of the Milky Way with respect to the microwave background, and the flattening of the Local Supercluster can be successfully accounted for by these models, provided that the initial perturbation is sufficiently flattened. Viable models are obtained only if the ratio of the lengths of the two smaller axes of the initial perturbation is at least 3:1 in an Einstein-de Sitter universe or at least 1.8:1 in a universe for which the density parameter (Omega) is of order 0.1, when the protocluster pancakes.

White, S. D. M.↗
NASA NTRS1974

An analytic method to account for drag in the Vinti Satellite theory

To retain separability in the Vinti theory of earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all altitudes and simultaneously reduced the variational equations to indefinite integrals with closed form evaluations. The values of the limits for any arbitrary time interval are obtained from the Vinti program.

Watson, J. S.↗
NASA NTRS1977

The use of a movable telescoping end mass system for the time-optimal control of spinning spacecraft

The time-optimal control of a spin-stabilized spacecraft with a movable telescoping appendage (boom) is considered analytically and numerically. The motion of a control mass at the end of the boom is determined such that the terminal time will be minimized for two-axis control of a symmetric spacecraft. The equations of rotational motion are linearized about the desired state of spin about the symmetry axis. The equations for the transverse angular velocity components have the form of a coupled two dimensional harmonic oscillator with boom motion as a control force. The control function which brings the system to the desired state is known to be a series of positive and negative pulses. If the initial state is such that the system can be driven to rest in a single switch, the responses, switching and final times, and required boom motion may be determined analytically. Some typical numerical results based on these solutions are discussed.

Bainum, P. M.↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗
NASA NTRS1975

Some procedures for computerized electronic data processing of absorption measurements from artificial earth satellites

The processing of data obtained from solar absorption radiation measurements is discussed. The position of the satellite was obtained by numerical integration of the differential equations of motion using initial conditions. The position of the sun was calculated as a function of time, and the tangential elevation was determined approximately from the positions of the satellite and the sun. The coefficients of an approximation formula and of a data smoothing process were determined, and the inversion of an Abel integral equation is solved analytically.

Trinkkeller, B.↗
NASA NTRS1992

Study of explosive and nonexplosive cyclogenesis during FGGE

Explosive cyclogenesis during the winter of the First Global GARP Experiment (January-February 1979) is analyzed using the revised European Centre for Medium Range Weather Forecasts (ECMWF) analyses. Explosive cyclogenesis is defined as a decrease in the sea level pressure at the rate of 1 mb/h for at least 12 h. Diagnostics for 23 explosively developing cases and 16 nonexplosive cases are evaluated. Parameters compared include the dry static stability, low-level relative vorticity, vorticity advection, upper-level divergence, and kinematic vertical velocities. These parameters are compared statistically at the initial, 12-, and 24-h time periods. Parameters for which the explosive and nonexplosive cyclone ensembles were statistically separable are the kinematic vertical velocity and the upper-level divergence and vorticity advection. The strong upper-level processes for the explosive cases at the initial time indicate the importance of upper-tropospheric features in producing the stronger vertical motions and more rapid cyclogenesis.

Wash, Carlyle H.↗
NASA NTRS1982

Methods of sequential estimation for determining initial data in numerical weather prediction

Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.

Cohn, S. E.↗
NASA NTRS1976

Coupled base motion response analysis of payload structural systems

Coupled base motion response analysis of payload structural systems is discussed. A systems analysis program is described which by component analysis structural transient response analyses can be completed. The program presents a proven technique, used initially on the Skylab program, which is designed to reduce cost and schedule time on detail structural analyses of structural payload systems. Base motion procedures are employed where critical segments of complex structural systems or components may be analyzed for various load conditions without having to re-establish the entire structural system coupled model properties. The transient response characteristics of a complex structural system are used as a basis for evaluating the transient response of a similar system.

Devers, A. D.↗
DOE OSTI2026

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER↗
NASA NTRS1986

Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension

The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.

Natarajan, R.↗
NASA NTRS1987

Analysis of photopole data reduction models

An analysis of the total impulse obtained from a buried explosive charge can be calculated from displacement versus time points taken from successive film frames of high speed motion pictures of the explosive event. The indicator of that motion is a pole and baseplate (photopole), which is placed on or within the soil overburden. Here, researchers are concerned with the precision of the impulse calculation and ways to improve that precision. Also examined here is the effect of each initial condition on the curve fitting process. It is shown that the zero initial velocity criteria should not be applied due to the linear acceleration versus time character of the cubic power series. The applicability of the new method to photopole data records whose early time motions are obscured is illustrated.

Cheek, James B.↗
NASA NTRS2006

Adaptive Changes In Postural Equilibrium And Motion Sickness Following Repeated Exposures To Virtual Environments

Virtual environments offer unique training opportunities, particularly for training astronauts and preadapting them to the novel sensory conditions of microgravity. Two unresolved human factors issues in virtual reality (VR) systems are: 1) potential "cybersickness", and 2) maladaptive sensorimotor performance following exposure to VR systems. Interestingly, these aftereffects are often quite similar to adaptive sensorimotor responses observed in astronauts during and/or following space flight. Changes in the environmental sensory stimulus conditions and the way we interact with the new stimuli may result in motion sickness, and perceptual, spatial orientation and sensorimotor disturbances. Initial interpretation of novel sensory information may be inappropriate and result in perceptual errors. Active exploratory behavior in a new environment, with resulting feedback and the formation of new associations between sensory inputs and response outputs, promotes appropriate perception and motor control in the new environment. Thus, people adapt to consistent, sustained alterations of sensory input such as those produced by microgravity, unilateral labyrinthectomy and experimentally produced stimulus rearrangements. Adaptation is revealed by aftereffects including perceptual disturbances and sensorimotor control disturbances. The purpose of the current study was to compare disturbances in postural control produced by dome and head-mounted virtual environment displays, and to examine the effects of exposure duration, and repeated exposures to VR systems. Forty-one subjects (21 men, 20 women) participated in the study with an age range of 21-49 years old. One training session was completed in order to achieve stable performance on the posture and VR tasks before participating in the experimental sessions. Three experimental sessions were performed each separated by one day. The subjects performed a navigation and pick and place task in either a dome or head-mounted display (HMD) VR system for either 30 or 60 min. The environment was a square room with 15 pedestals on two opposite walls. The objects appeared on one set of pedestals and the subject s objective was to move the objects to the other set of pedestals. After the subject picked up an object, a pathway appeared and they were required to follow the pathway to the other side of the room. The subject was instructed to perform the task as quickly and accurately as possible, avoiding hitting walls and other any obstacles and placing the object on the center of the pedestal. Postural equilibrium was measured (using the Equitest CDP balance system, Neurocom, International) before, immediately after, and at 1 hr, 2 hr, 4 hr and 6 hr following exposure to VR. Postural equilibrium was measured during quiet stance with eyes open, eyes closed and vision and/or ankle proprioceptive inputs selectively altered by servo-controlling the visual surround and/or support surface to the subject s center of mass sway. Posture data was normalized using a log transformation and motion sickness data were normalized using the square root. In general, we found that exposure to VR resulted in decrements in postural stability. The largest decrements were observed in the tests performed immediately following exposure to VR and showed a fairly rapid recovery across the remaining test sessions. In addition, subjects generally showed improvement across days. We found significant main effects for day and time for the composite equilibrium score and for sensory organization tests (SOT) 1, 2 and 6. Significant main effects were observed for day for SOT 3 and 5. Although we found no significant main effects for gender (when center of gravity was used as a covariate), we did observe significant gender X time interaction effects for composite equilibrium and for SOT 1, 3, 4 and 5. Women appeared to show larger decrements in postural stability immediately after exposure to VR than men, but recover more quickly than n. Finally, we found no significant main effects for type of VR device or for exposure duration, however, these factors did interact with other factors during some of the SOTs. Subjects exhibited rapid recovery of motion sickness symptoms across time following exposure to VR and significantly less severe symptoms across days. We did not observe main effects for gender, type of device or duration of exposure. Individuals recovered from the detrimental effects of exposure to virtual reality on postural control and motion sickness within one hour. Sickness severity and initial decrements in postural equilibrium decreases over days, which suggests that subjects become dual-adapted over time. These findings provide some direction for developing training schedules for VR users that facilitate adaptation, and support the idea that preflight training of astronauts may serve as useful countermeasure for the sensorimotor effects of space flight.

Harm, D. L.↗
NASA NTRS1990

Numerical simulation of solar coronal magnetic fields

Many aspects of solar activity are believed to be due to the stressing of the coronal magnetic field by footpoint motions at the photosphere. The results are presented of a fully spectral numerical simulation which is the first 3-D time dependent simulation of footpoint stressing in a geometry appropriate for the corona. An arcade is considered that is initially current-free and impose a smooth footpoint motion that produces a twist in the field of approx 2 pi. The footprints were fixed and the evolution was followed until the field relaxes to another current-free state. No evidence was seen for any instability, either ideal or resistive and no evidence for current sheet formation. The most striking feature of the evolution is that in response to photospheric motions, the field expands rapidly upward to minimize the stress. The expansion has two important effects. First, it suppresses the development of dips in the field that could support dense, cool material. For the motions assumed, the magnetic field does not develop a geometry suitable for prominence formation. Second, the expansion inhibits ideal instabilities such as kinking. The results indicate that simple stearing of a single arcade is unlikely to lead to solar activity such as flares or prominences. Effects are discussed that might possibly lead to such activity.

Dahlburg, Russell B.↗
NASA NTRS1993

Solving modal equations of motion with initial conditions using MSC/NASTRAN DMAP. Part 1: Implementing exact mode superposition

Within the MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) module TRD1, solving physical (coupled) or modal (uncoupled) transient equations of motion is performed using the Newmark-Beta or mode superposition algorithms, respectively. For equations of motion with initial conditions, only the Newmark-Beta integration routine has been available in MSC/NASTRAN solution sequences for solving physical systems and in custom DMAP sequences or alters for solving modal systems. In some cases, one difficulty with using the Newmark-Beta method is that the process of selecting suitable integration time steps for obtaining acceptable results is lengthy. In addition, when very small step sizes are required, a large amount of time can be spent integrating the equations of motion. For certain aerospace applications, a significant time savings can be realized when the equations of motion are solved using an exact integration routine instead of the Newmark-Beta numerical algorithm. In order to solve modal equations of motion with initial conditions and take advantage of efficiencies gained when using uncoupled solution algorithms (like that within TRD1), an exact mode superposition method using MSC/NASTRAN DMAP has been developed and successfully implemented as an enhancement to an existing coupled loads methodology at the NASA Lewis Research Center.

Abdallah, Ayman A.↗
NASA NTRS1996

Sensor-Based Collision Avoidance: Theory and Experiments

A new on-line control strategy for sensor-based collision avoidance of manipulators and supporting experimental results are presented in this article. This control strategy is based on nullification of virtual forces applied to the end-effector by a hypothetical spring-plus-damper attached to the object's surface. In the proposed approach, the real-time arm control software continuously monitors the object distance measured by the arm-mounted proximity sensors. When this distance is less than a preset threshold, the collision avoidance control action is initiated to inhibit motion toward the object and thus prevent collision. This is accomplished by employing an outer feedback loop to perturb the end-effector nominal motion trajectory in real-time based on the sensory data. The perturbation is generated by a proportional-plus-integral (PI) collision avoidance controller acting on the difference between the sensed distance and the preset threshold. This approach is computationally very fast, requires minimal modification to the existing manipulator positioning system, and provides the manipulator with an on-line collision avoidance capability to react autonomously and intelligently. A dexterous RRC robotic arm is instrumented with infrared proximity sensors and is operated under the proposed collision avoidance strategy. Experimental results are presented to demonstrate end-effector collision avoidance both with an approaching object and while reaching inside a constricted opening.

Seraji, Homayoun↗
DOE OSTI2025

Control-Affine Schrödinger Bridge and Generalized Bohm Potential

From a stochastic control perspective, the Schrödinger bridge is a density-valued continuous curve parameterized by time that connects a given pair of initial and terminal probability densities via minimum effort controlled Brownian motion. The control-affine Schrödinger bridge extends this idea to a generic control-affine Itô diffusion, possibly with an additive state cost. Here, in this letter, we recast the necessary conditions of optimality for the control-affine Schrödinger bridge problem as a two point boundary value problem for a quantum mechanical Schrödinger PDE with complex potential. This complex-valued potential is a generalization of the real-valued Bohm potential in quantum mechanics. Our derived potential is akin to the optical potential in nuclear physics where the real part of the potential encodes elastic scattering (transmission of wave function), and the imaginary part encodes inelastic scattering (absorption of wave function). The key takeaway is that the process noise that drives the evolution of probability densities induces an absorbing medium in the evolution of wave function. These results make new connections between control theory and non-equilibrium statistical mechanics through the lens of quantum mechanics.

Markov processes↗
NASA NTRS1975

Attitude determination of a high altitude balloon system. Part 2: Development of the parameter determination process

The attitude of the balloon system is determined as a function of time if: (a) a method for simulating the motion of the system is available, and (b) the initial state is known. The initial state is obtained by fitting the system motion (as measured by sensors) to the corresponding output predicted by the mathematical model. In the case of the LACATE experiment the sensors consisted of three orthogonally oriented rate gyros and a magnetometer all mounted on the research platform. The initial state was obtained by fitting the angular velocity components measured with the gyros to the corresponding values obtained from the solution of the math model. A block diagram illustrating the attitude determination process employed for the LACATE experiment is shown. The process consists of three essential parts; a process for simulating the balloon system, an instrumentation system for measuring the output, and a parameter estimation process for systematically and efficiently solving the initial state. Results are presented and discussed.

Nigro, N. J.↗