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DOE OSTI2024

Lagrangian formulation of nuclear–electronic orbital Ehrenfest dynamics with real-time TDDFT for extended periodic systems

Here, we present a Lagrangian-based implementation of Ehrenfest dynamics with nuclear–electronic orbital (NEO) theory and real-time time-dependent density functional theory for extended periodic systems. In addition to a quantum dynamical treatment of electrons and selected protons, this approach allows for the classical movement of all other nuclei to be taken into account in simulations of condensed matter systems. Furthermore, we introduce a Lagrangian formulation for the traveling proton basis approach and propose new schemes to enhance its application for extended periodic systems. Validation and proof-of-principle applications are performed on electronically excited proton transfer in the o-hydroxybenzaldehyde molecule with explicit solvating water molecules. These simulations demonstrate the importance of solvation dynamics and a quantum treatment of transferring protons. This work broadens the applicability of the NEO Ehrenfest dynamics approach for studying complex heterogeneous systems in the condensed phase.

Calculus of variations↗

NASA NTRS1990

On-orbit structural dynamic performance of a 15-meter microwave radiometer antenna

The on-orbit structural dynamic performance of a microwave radiometer antenna for Earth science applications is addressed. The radiometer is one of the Earth-observing instruments aboard a proposed geostationary platform as part of the Mission to the Planet Earth. A sequential approach is presented for assessing the ability of an antenna structure to retain its geometric shape subject to a representative onboard disturbance. This approach includes establishing the structural requirements of the antenna, developing the structural and disturbance models, performing modal and forced response analyses, and evaluating the resulting distortions in terms of the antenna's ability to meet stringent structural performance requirements. Two antenna configurations are discussed: free-flying and platform-mounted. These configurations are analyzed for a representative disturbance function which simulates rotation of the subreflector in order to perform a raster-type scan of the Earth disk. Results show that the scanning maneuver modeled would not induce antenna structural errors outside the specified limits.

Wahls, Deborah M.↗

NASA NTRS2017

Operating Small Sat Swarms as a Single Entity: Introducing SODA

NASA's decadal survey determined that simultaneous measurements from a 3D volume of space are advantageous for a variety of studies in space physics and Earth science. Therefore, swarm concepts with multiple spacecraft in close proximity are a growing topic of interest in the small satellite community. Among the capabilities needed for swarm missions is a means to maintain operator-specified geometry, alignment, or separation. Swarm stationkeeping poses a planning challenge due to the limited scalability of ground resources. To address scalable control of orbital dynamics, we introduce SODA - Swarm Orbital Dynamics Advisor - a tool that accepts high-level configuration commands and provides the orbital maneuvers needed to achieve the desired type of swarm relative motion. Rather than conventional path planning, SODA's innovation is the use of artificial potential functions to define boundaries and keepout regions. The software architecture includes high fidelity propagation, accommodates manual or automated inputs, displays motion animations, and returns maneuver commands and analytical results. Currently, two swarm types are enabled: in-train distribution and an ellipsoid volume container. Additional swarm types, simulation applications, and orbital destinations are in planning stages.

Conn, Tracie↗

NASA NTRS2017

Operating Small Sat Swarms as a Single Entity: Introducing SODA

Conn, Tracie↗

NASA NTRS1974

Development and correlation: Viking Orbiter analytical dynamic model with modal test

The Viking Orbiter (VO) experience in the achievement of a mathematical model is described along with the following project activities: (1) the generation of the overall plan for load analysis, an analytical dynamic model, and development tests; (2) the performance of VO subsystem static and modal tests; and (3) the correlation of the VO system model analysis and test. Success is attributed to the coordination of analysis and test using substructure modal coupling techniques.

Wada, B. K.↗

NASA NTRS2017

Operating Small Sat Swarms as a Single Entity: Introducing SODA

Swarm concepts are a growing topic of interest in the small satellite community. Compared to a small satellite constellation, a swarm has the distinction of being multiple spacecraft in close proximity, in approximately the same orbit. Furthermore, we envision swarms to have capabilities for cross-link communication and station-keeping. Of particular interest is a means to maintain operator-specified geometry, alignment, and/or separation.From NASA's decadal survey, it is clear that simultaneous measurements from a 3D volume of space are desired for a variety of Earth scientific studies. As this mission concept is ultimately extended to deep space, some degree of local control for the swarm to self-correct its configuration is required. We claim that the practicality of ground commanding each individual satellite in the swarm is simply not a feasible concept of operations. In other words, the current state-of-practice does not scale to very large swarms (e.g. 100 spacecraft or more) without becoming cost prohibitive. To contain the operations costs and complexity, a new approach is required: the swarm must be operated as a unit, responding to high-level specifications for relative position and velocity.The Mission Design Division at NASA Ames Research Center is looking to the near future for opportunities to develop satellite swarm technology. As part of this effort, we are developing SODA (Swarm Orbital Dynamics Advisor), a tool that provides the orbital maneuvers required to achieve a desired type of relative swarm motion. The purpose of SODA is two-fold. First, it encompasses the algorithms and orbital dynamics model to enable the desired relative motion of the swarm satellites. The process starts with the user specifying the properties of a swarm configuration. This could be as simple as varying in-track spacing of the swarm in one orbit, or as complex as maintaining a specified 3D geometrical orientation. We presume that science objectives will drive this choice. Given these inputs, the tool provides the most efficient maneuver(s) to achieve the objective.Second, SODA provides a variety of visualization tools. We acknowledge that the relationship between a desired relative motion amongst the swarm, and the corresponding orbital parameters for each individual satellite may not be immediately apparent for ground controllers and mission planners. The purpose of SODA's visualization tools is to illustrate this concept clearly with a variety of graphics and animations. After computing the optimal orbital maneuvers to modify the swarm, these results are simulated to demonstrate successful swarm control.Our emphasis in this paper is on the importance of relating the desired motion of the swarm satellites relative to one another with the required orbital element changes. One cannot joystick a drifting swarm satellite back into position; the underlying orbital mechanics dictate the most efficient recovery maneuvers. To illustrate this point, results from several case study simulations are presented. We conclude with our forward work for ongoing SODA development and potential science applications.

small satellites↗

NASA NTRS1972

Study of the dynamics of orbital assemblies including interactions with geometrical appendages

Computer programs are provided for the simulation of a unified flexible spacecraft relative to the dynamics of orbital assemblies, including interactions with geometrical appendages. The CDC 6500 and Univac 1108 computers are used with FORTRAN. The software and hardware requirements are described and diagrammed, as well as the overall deck set-up. A list of standard and nonstandard routines is also included.

Hull, G.↗

NASA NTRS1982

On the modelling and simulation of the dynamics and control of large flexible orbiting systems

This paper attempts to review the steps involved in the development of mathematical models that can be used to simulate the in-orbit dynamics of large flexible systems. The use of graph theoretic techniques can often be used to reduce the computational effort involved for calculating the eigenvalues of large ordered systems. Computer generated graphical techniques may provide additional insight into the understanding of elastic modal shape functions of complex systems. Finally the numerical techniques commonly used to develop shape and attitude control laws will be briefly reviewed.

Bainum, P. M.↗

NASA NTRS2005

Adjoint Sensitivity Analysis of Orbital Mechanics: Application to Computations of Observables' Partials with Respect to Harmonics of the Planetary Gravity Fields

An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.

gravity fields↗

DOE OSTI2021

Excited State Intramolecular Proton Transfer with Nuclear-Electronic Orbital Ehrenfest Dynamics

The recent development of the Ehrenfest dynamics approach in the nuclear-electronic orbital (NEO) framework provides a promising way to simulate coupled nuclear-electronic dynamics. Our previous study showed that the NEO-Ehrenfest approach with a semi- classical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. In this work, we provide a more thorough analysis of the semiclassical traveling proton basis method to elucidate its validity and convergence behavior. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool to provide insights and predictions for these processes.

Zhao, Luning↗

NASA NTRS2013

Dynamics of Orbits near 3:1 Resonance in the Earth-Moon System

The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth with a period near 3:1 resonance with the Moon. Its orbit is oriented so that apogee does not approach the Moon. Simulations show this orbit to be remarkably stable over the next twenty years. This article examines the dynamics of such orbits in the Circular Restricted 3-Body Problem (CR3BP). We look at three types of periodic orbits, each exhibiting a type of symmetry of the CR3BP. For each of the orbit types, we assess the local stability using Floquet analysis. Although not all of the periodic solutions are stable in the mathematical sense, any divergence is so slow as to produce practical stability over several decades. We use Poincare maps with twenty-year propagations to assess the nonlinear stability of the orbits, where the perturbation magnitudes are related to the orbit uncertainty for the IBEX mission. Finally we show that these orbits belong to a family of orbits connected in a bifurcation diagram that exhibits exchange of stability. The analysis of these families of period orbits provides a valuable starting point for a mission orbit trade study.

Dichmann, Donald J.↗

NASA NTRS1995

(abstract) Satellite Dynamics About Eros

The Near Earth Asteroid Rendezvous (NEAR) mission spacecraft will arrive at Asteroid 433 (Eros) in February 1999. Following an initial period of characterization, the science phase of the mission will commence, and unprecedented information concerning an asteroid's shape, mass, density, composition, and rotational dynamics will be sent to Earth for analysis. It will also mark the start of orbital operations about the most complex and irregular gravity field ever encountered in the history of space exploration. The severity of Eros' distortion from the usual spheroid bodies encountered in planetary exploration leads to fundamental differences in the orbital dynamics about it. Operations about Eros will also serve as an exciting test of orbital determination and prediction in an orbital environment which can be chaotic in some instances. General orbital dynamics about Eros are discussed. Some simple formulae are given for the secular motion of the node and argument of periapsis. Conditions for a satellite orbit to escape from Eros are discussed, and some simple results derived. Finally, the chaotic nature of certain orbits about Eros are discussed, and the consequences for orbit prediction are investigated.

Near↗

NASA NTRS1999

Inversion of Gravity Fields From the Spacecraft Orbital Data Using an Adjoint Operator Approach

In perturbation approximation, the forward problem of orbital dynamics (equations with initial conditions) is linear with respect to variations of coordinates and/or velocities of the spacecraft and to corresponding variations of the gravity field in the models used. The linear operator adjoint to the linear operator of such forward problem turns out to be instrumental in inversion of differences between observed and predicted coordinates/velocities in terms of the updates of harmonics in the initial gravity field model. Based on this approach, the solution of resulting adjoint problem of orbital dynamics can be used to directly evaluate the matrix of partial derivatives of observable differences with respect to the gravity field harmonics. General discussion of the adjoint problem of orbital dynamics is given and an example of a mathematical formalism for the practical retrieval algorithm is presented.

Ustinov, E. A.↗

NASA NTRS2016

Engineering Considerations Applied to Starshade Repointing

Engineering analysis has been carried out on orbit dynamics that drive the delta-v budget for repointing a free-flying starshade occulter for viewing exoplanets with a space telescope. This analysis has application to the design of starshade spacecraft and yield calculations of observations of exoplanets using a space telescope and a starshade. Analysis was carried out to determine if there may be some advantage for the global delta-v budget if the telescope performs orbit changing delta-v maneuvers as part of the telescope-starshade alignment for observing exoplanets. Analysis of the orbit environmental forces at play found no significant advantage in having the telescope participate in delta-v maneuvers for exoplanet observation repointing. A separate analysis of starshade delta-v for repointing found that the orbit dynamics of the starshade is driven by multiple simultaneous variables that need to be considered together in order to create an effective estimate of delta-v over an exoplanet observation campaign. These include area of the starshade, dry mass of the starshade spacecraft, and propellant mass of the starshade spacecraft. Solar radiation pressure has the potential to play a dominant role in the orbit dynamics and delta-v budget. SRP effects are driven by the differences in the mass, area, and coefficients of reflectivity of the observing telescope and the starshade. The propellant budget cannot be effectively estimated without a conceptual design of a starshade spacecraft including the propulsion system. The varying propellant mass over the mission is a complexity that makes calculating the propellant budget less straightforward.

delta-V↗

NASA NTRS2006

Dynamics of Orbital Masses in an Unbalanced Rotor

Historically, orbital masses have been used as automatic balancers in rotating machines. However, in these applications, the masses are free to move and rotate with the rotor from zero to operating speeds. For gas turbine applications it is desirable for the orbital masses to be fixed and unmoving, until their release from a sudden unbalance at the operating speed, such as occurs from a blade-out event. The objective of this work is to develop the dynamical equations of motion for orbital masses on a rotating shaft. In subsequent work these equations will be incorporated into a rotor structural dynamics computer code and the feasibility of attenuating rotor unbalance response with orbital masses will be investigated.

Gallardo, Vicente↗

NASA NTRS2011

On-Orbit Solar Dynamics Observatory (SDO) Star Tracker Warm Pixel Analysis

This paper describes the process of identification and analysis of warm pixels in two autonomous star trackers on the Solar Dynamics Observatory (SDO) mission. A brief description of the mission orbit and attitude regimes is discussed and pertinent star tracker hardware specifications are given. Warm pixels are defined and the Quality Index parameter is introduced, which can be explained qualitatively as a manifestation of a possible warm pixel event. A description of the algorithm used to identify warm pixel candidates is given. Finally, analysis of dumps of on-orbit star tracker charge coupled devices (CCD) images is presented and an operational plan going forward is discussed. SDO, launched on February 11, 2010, is operated from the NASA Goddard Space Flight Center (GSFC). SDO is in a geosynchronous orbit with a 28.5 inclination. The nominal mission attitude points the spacecraft X-axis at the Sun, with the spacecraft Z-axis roughly aligned with the Solar North Pole. The spacecraft Y-axis completes the triad. In attitude, SDO moves approximately 0.04 per hour, mostly about the spacecraft Z-axis. The SDO star trackers, manufactured by Galileo Avionica, project the images of stars in their 16.4deg x 16.4deg fields-of-view onto CCD detectors consisting of 512 x 512 pixels. The trackers autonomously identify the star patterns and provide an attitude estimate. Each unit is able to track up to 9 stars. Additionally, each tracker calculates a parameter called the Quality Index, which is a measure of the quality of the attitude solution. Each pixel in the CCD measures the intensity of light and a warns pixel is defined as having a measurement consistently and significantly higher than the mean background intensity level. A warns pixel should also have lower intensity than a pixel containing a star image and will not move across the field of view as the attitude changes (as would a dim star image). It should be noted that the maximum error introduced in the star tracker attitude solution during suspected warm pixel corruptions is within the specified 36 attitude error budget requirement of [35, 70, 70] arcseconds. Thus, the star trackers provided attitude accuracy within the specification for SDO. The star tracker images are intentionally defocused so each star image is detected in more than one CCD pixel. The position of each star is calculated as an intensity-weighted average of the illuminated pixels. The exact method of finding the positions is proprietary to the tracker manufacturer. When a warm pixel happens to be in the vicinity of a star, it can corrupt the calculation of the position of that particular star, thereby corrupting the estimate of the attitude.

Felikson, Denis↗

NASA NTRS1994

Particle acceleration in the dynamic magnetotail: Orbits in self-consistent three-dimensional MHD fields

The acceleration of protons in a dynamically evolving magnetotail is investigated by tracing particles in the fields obtained from a three-dimensional resistive magnetohydrodynamic (MHD) simulation. The MHD simulation, representing plasmoid formation and ejection through a near-Earth reconnection process, leads to cross-tail electric fields of up to approximately 4 mV/m with integrated voltages across the tail of up to approximately 200 kV. Energization of particles takes place over a wide range along the tail, due to the large spatial extent of the increased electric field together with the finite cross-tail extent of the electric field region. Such accelerated particles appear earthward of the neutral line over a significant portion of the closed field line region inside of the separatrix, not just in the vicinity of the separatrix. Two different acceleration processes are identified: a 'quasi-potential' acceleration, due to particle motion in the direction of the cross-tail electric field, and a 'quasi-betatron' effect, which consists of multiple energy gains from repeated crossings of the acceleration region, mostly on Speiser-type orbits, in the spatially varying induced electric field. The major source region for accelerated particles in the hundreds of keV range is the central plasma sheet at the dawn flank outside the reconnection site. Since this source plasma is already hot and dense, its moderate energization by a factor of approximately 2 may be sufficient to explain the observed increases in the energetic particle fluxes. Particles from the tail are the source of beams at the plasma sheet/lobe boundary. The temporal increase in the energetic particle fluxes, estimated from the increase in energy gain, occurs on a fast timescale of a few minutes, coincident with a strong increase in B(sub z), despite the fact that the inner boundary ('injection boundary') of the distribution of energized particles is fairly smooth.

Birn, Joachim↗

NASA NTRS2009

A Process for Comparing Dynamics of Distributed Space Systems Simulations

The paper describes a process that was developed for comparing the primary orbital dynamics behavior between space systems distributed simulations. This process is used to characterize and understand the fundamental fidelities and compatibilities of the modeling of orbital dynamics between spacecraft simulations. This is required for high-latency distributed simulations such as NASA s Integrated Mission Simulation and must be understood when reporting results from simulation executions. This paper presents 10 principal comparison tests along with their rationale and examples of the results. The Integrated Mission Simulation (IMSim) (formerly know as the Distributed Space Exploration Simulation (DSES)) is a NASA research and development project focusing on the technologies and processes that are related to the collaborative simulation of complex space systems involved in the exploration of our solar system. Currently, the NASA centers that are actively participating in the IMSim project are the Ames Research Center, the Jet Propulsion Laboratory (JPL), the Johnson Space Center (JSC), the Kennedy Space Center, the Langley Research Center and the Marshall Space Flight Center. In concept, each center participating in IMSim has its own set of simulation models and environment(s). These simulation tools are used to build the various simulation products that are used for scientific investigation, engineering analysis, system design, training, planning, operations and more. Working individually, these production simulations provide important data to various NASA projects.

Cures, Edwin Z.↗