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NASA NTRS1984

Elimination of uncontrollable rigid body mode, appendix C

The planar system model is examined which reveals two rigid body modes. One is due to the pure translation of the whole experiment assembly and is uncontrollable because the only control input is a torque at the gimbal. The other rigid body mode is due to the pointing of the gimbal and is the one for which control is sort. The problem arises from the Vector V2 which relates the control input to the modal coordinates. Since its fifth and sixth elements are both nonzero, neither body mode can be thrown away as is. The two rigid body modes must be transformed so that one is unaffected by the control input and one is left controllable. The uncontrollable mode can then be eliminated from the model for design purposes. A process is described to accomplish the elimination of the uncontrollable rigid body mode.

Source record↗

NASA NTRS1986

Variation of cosmic rays and solar wind properties with respect to the heliospheric current sheet. II - Rigidity dependence of the latitudinal gradient of cosmic rays at 1 AU

The role which empirical determinations of the latitudinal variation of cosmic rays with respect to the current sheet may have in illuminating the importance of the cross-field drift of particles in the large-scale heliospheric magnetic field is discussed. Using K coronameter observations and measured solar wind speeds, the latitudinal gradients have been determined with respect to the current sheet for cosmic rays in four rigidity ranges. Gradients vary between approximately -2 and -50 pct/AU. The rigidity dependence of the decrease of cosmic ray flux with distance from the current sheet lies between the -0.72 to -0.86 power of the rigidity, with the exact dependence being determined by the definition used for the median rigidity of each monitor.

Newkirk, G., Jr.↗

NASA NTRS1987

Minimum time attitude slewing maneuvers of a rigid spacecraft

The problems of large-angle attitude maneuvers of a spacecraft have gained much consideration in recent years. The configurations of the spacecraft considered are: completely rigid, a combination of rigid and flexible parts, or gyrostat-type systems. The performance indices usually include minimum torque integration, power criterion, and frequency-shaped cost functionals. The minimum time slewing problem of a rigid spacecraft was examined. Optimal control theory (Maximum Principal) was applied to the slewing motion of a general rigid spacecraft. Control torque about all three axes was computed. The equations for the system are composed of the Euler dynamical equations in the spacecraft body axes and the quaternion kinematical equation. By introducing the costates for the quaternion and the angular velocity, the Hamiltonian of the system can be formed and the optimal control obtained. Finally the methods are applied to the SCOLE slewing motion. The control variables include three control moments on the Shuttle and two control forces on the reflector. Numerical results are discussed.

Li, Feiyue↗

NASA NTRS1987

The origin of rigidly rotating magnetic field patterns on the sun

Using analytical calculations and numerical simulations, it is shown that a meridional component of magnetic-flux transport will offset the shearing effect of differential rotation and give rise to rigidly rotating patterns of large-scale magnetic field. The nonaxisymmetric field attains a striped polarity pattern which rotates rigidly like a barber pole while its individual small-scale flux elements rotate at the differential rate of the latitudes they are crossing. On the sun, the meridional transport is provided by supergranular diffusion possibly assisted by a small poleward flow. New sources of flux retard this process and exclude the rigid rotation from the sunspot belts until well into the declining phase of the sunspot cycle. This mechanism accounts for a number of heretofore unexplained phenomena including the tendency for coronal holes to rotate rigidly during the declining phase of the sunspot cycle.

Sheeley, N. R., Jr.↗

NASA NTRS1990

Interactions between rigid-body and flexible-body motions in maneuvering spacecraft

The present consideration of the significant interactions between rigid-body and flexible-body motions in maneuvering spacecraft proceeds by distinguishing between the two types of motion on the basis of a tracking coordinate system which coincides with the rigid-body component of the motion, as well as by maintaining the motion relative to the tracking coordinate as orthogonal to the rigid-body motion. The elastic motion is excited by the rigid-body motion via Coriolis terms, angular acceleration terms, and centrifugal terms. These interactions are illustrated for spacecraft undergoing bidirectional elastic motions via the dynamics of constantly rotating free-free beams subject to combined bending and longitudinal vibration.

Silverberg, Larry M.↗

NASA NTRS1990

A boundary integral approach to the scattering of nonplanar acoustic waves by rigid bodies

The acoustic scattering of an incident wave by a rigid body can be described by a singular Fredholm integral equation of the second kind. This equation is derived by solving the wave equation using generalized function theory, Green's function for the wave equation in unbounded space, and the acoustic boundary condition for a perfectly rigid body. This paper will discuss the derivation of the wave equation, its reformulation as a boundary integral equation, and the solution of the integral equation by the Galerkin method. The accuracy of the Galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources. From the analysis of these simpler cases, the accuracy of the Galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere. The solution by the Galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder. This is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages.

Gallman, Judith M.↗

NASA NTRS1993

Analytic Theory and Control of the Motion of Spinning Rigid Bodies

Numerical simulations are often resorted to, in order to understand the attitude response and control characteristics of a rigid body. However, this approach in performing sensitivity and/or error analyses may be prohibitively expensive and time consuming, especially when a large number of problem parameters are involved. Thus, there is an important role for analytical models in obtaining an understanding of the complex dynamical behavior. In this dissertation, new analytic solutions are derived for the complete attitude motion of spinning rigid bodies, under minimal assumptions. Hence, we obtain the most general solutions reported in the literature so far. Specifically, large external torques and large asymmetries are included in the problem statement. Moreover, problems involving large angular excursions are treated in detail. A new tractable formulation of the kinematics is introduced which proves to be extremely helpful in the search for analytic solutions of the attitude history of such kinds of problems. The main utility of the new formulation becomes apparent however, when searching for feedback control laws for stabilization and/or reorientation of spinning spacecraft. This is an inherently nonlinear problem, where standard linear control techniques fail. We derive a class of control laws for spin axis stabilization of symmetric spacecraft using only two pairs of gas jet actuators. Practically, this could correspond to a spacecraft operating in failure mode, for example. Theoretically, it is also an important control problem which, because of its difficulty, has received little, if any, attention in the literature. The proposed control laws are especially simple and elegant. A feedback control law that achieves arbitrary reorientation of the spacecraft is also derived, using ideas from invariant manifold theory. The significance of this research is twofold. First, it provides a deeper understanding of the fundamental behavior of rigid bodies subject to body-fixed torques. Assessment of the analytic solutions reveals that they are very accurate; for symmetric bodies the solutions of Euler's equations of motion are, in fact, exact. Second, the results of this research have a fundamental impact on practical scientific and mechanical applications in terms of the analysis and control of all finite-sized rigid bodies ranging from nanomachines to very large bodies, both man made and natural. After all, Euler's equations of motion apply to all physical bodies, barring only the extreme limits of quantum mechanics and relativity.

Tsiotras, Panagiotis↗

NASA NTRS2001

Geomagnetic Cutoff Rigidity Computer Program: Theory, Software Description and Example

The access of charged particles to the earth from space through the geomagnetic field has been of interest since the discovery of the cosmic radiation. The early cosmic ray measurements found that cosmic ray intensity was ordered by the magnetic latitude and the concept of cutoff rigidity was developed. The pioneering work of Stoermer resulted in the theory of particle motion in the geomagnetic field, but the fundamental mathematical equations developed have 'no solution in closed form'. This difficulty has forced researchers to use the 'brute force' technique of numerical integration of individual trajectories to ascertain the behavior of trajectory families or groups. This requires that many of the trajectories must be traced in order to determine what energy (or rigidity) a charged particle must have to penetrate the magnetic field and arrive at a specified position. It turned out the cutoff rigidity was not a simple quantity but had many unanticipated complexities that required many hundreds if not thousands of individual trajectory calculations to solve. The accurate calculation of particle trajectories in the earth's magnetic field is a fundamental problem that limited the efficient utilization of cosmic ray measurements during the early years of cosmic ray research. As the power of computers has improved over the decades, the numerical integration procedure has grown more tractable, and magnetic field models of increasing accuracy and complexity have been utilized. This report is documentation of a general FORTRAN computer program to trace the trajectory of a charged particle of a specified rigidity from a specified position and direction through a model of the geomagnetic field.

Smart, D. F.↗

NASA NTRS2002

Finite Element Modeling of Deployment, and Foam Rigidization of Struts and Quarter Scale Shooting Star Experiment

Inflated cylindrical struts constructed of kapton polyimide film and rigidized with foam have considerable practical application and potential for use as components of inflatable concentrator assemblies, antenna structures and space power systems, Because of their importance, it is of great interest to characterize the dynamic behavior of these components and structures both experimentally and analytically. It is very helpful to take a building-block approach to modeling and understanding inflatable assemblies by first investigating in detail the behavior of the components such as the struts. The foam material used for rigidization of such cylinders has varying modulus, which is a function of different factors, such as density of the foam. Thus, the primary motivation of the tests and analytical modeling efforts was to determine and understand the response of foam-rigidized cylinders for different densities, sizes, and construction methods. In recent years, inflatable structures have been the subject of renewed interest for space applications such as communications antennae, solar thermal propulsion, and space solar power. A major advantage of using inflatable structures in space is that they are extremely lightweight. This makes inflatables a perfect match for solar thermal propulsion because of the low thrust levels available. An obvious second advantage is on-orbit deployability and subsequent space savings in launch configuration. It can be seen that inflatable cylindrical struts and torus are critical components of structural assemblies. In view of this importance, structural dynamic and static behaviors of typical rigidized polyimide struts are investigated in this paper. The paper will focus on the finite element models that were used to model the behavior of the complete solar collector structure, and the results that they provided, as compared to test data.

Larry Leigh, Jr.↗

NASA NTRS2011

Heat Transfer Measurement and Modeling in Rigid High-Temperature Reusable Surface Insulation Tiles

Heat transfer in rigid reusable surface insulations was investigated. Steady-state thermal conductivity measurements in a vacuum were used to determine the combined contribution of radiation and solid conduction components of heat transfer. Thermal conductivity measurements at higher pressures were then used to estimate the effective insulation characteristic length for gas conduction modeling. The thermal conductivity of the insulation can then be estimated at any temperature and pressure in any gaseous media. The methodology was validated by comparing estimated thermal conductivities with published data on a rigid high-temperature silica reusable surface insulation tile. The methodology was also applied to the alumina enhanced thermal barrier tiles. Thermal contact resistance for thermal conductivity measurements on rigid tiles was also investigated. A technique was developed to effectively eliminate thermal contact resistance on the rigid tile s cold-side surface for the thermal conductivity measurements.

Daryabeigi, Kamran↗

NASA NTRS2021

On the Rigidity Spectrum of Cosmic-Ray Variations within Propagating InterplanetaryDisturbances: Neutron Monitor and SOHO/EPHIN Observations at∼1–10GV

The rigidity dependence of all Forbush decreases (FDs) recorded from 1995 to 2015 has been determined using neutron monitor (NM) and Solar and Heliospheric Observatory (SOHO) (EPHIN) spacecraft data, covering the energy (rigidity) range from ∼433 MeV (1GV) to 9.10 GeV (10 GV). We analyzed a total of 421 events and determined the spectrum in rigidity with an inverse power-law fit. As a result, the mean spectral index was identified to be 〈γF〉 = 0.46 ± 0.02. The majority (∼66%) of the FDs have γF within the range 0.3–0.7. The remaining one-third of the events (∼33%) have either (very) soft or hard FD spectra, with the latter being more common than the former. Significant variations of γF occur within almost every FD event. During the initial FD decay phase the spectrum becomes gradually harder, in contrast to the recovery phase, when it becomes softer. Additionally, low energies (rigidities) seem to be better suited for studying the fine structure of interplanetary disturbances (primarily interplanetary coronal mass ejections) that lead to FDs. In particular, FDs recorded by the EPHIN instrument on SOHO better capture a two-step structure than FDs observed by NMs. Finally, the ejecta of an ICME, especially when identified as a magnetic cloud, often leads to abrupt changes in the slope of γF.

Anatoly Belov↗

NASA NTRS2022

Finite Element Modeling of Rigid-Flex PCB Robotic Structures for Dynamic Environments

Rigid-flex circuit boards are becoming moreprevalent as the limits are pushed on the size, mass, and geometryof electronic systems. A key aspect of designing a rigid-flexprinted circuit boards (PCB) system is an assessment of thedynamic properties of the PCB and predicting system perfor-mance under dynamic loading. Among current modeling method-ologies for rigid-flex PCB, a simplified modeling methodology thatadequately captures the system dynamics does not exist. This arti-cle presents a novel, computationally efficient approach formodeling rigid-flex PCB systems and the calibration of the mate-rial models via modal testing. The resulting simplified model isable to capture system frequencies, mode shapes, and representa-tive force-displacement behavior. The proposed methodology isused to model NASA Jet Propulsion Laboratory’s Pop-Up FlatFolding Explorer Robot (PUFFER) and assess the sensitivity of asystem model to input parameters.

John Bell↗

DOE OSTI2024

Rigidity‐Driven Structural Isomers in the NaCl–Ga 2 S 3 System: Implications for Energy Storage

Alternative energy sources require the search for innovative materials with promising functionalities. Systems with unusual chemical properties represent an insufficiently explored domain, concealing unexpected features. Using diffraction and Raman spectroscopy over a wide temperature range, supported by first‐principles simulations, a rare phenomenon is unveiled: phase‐dependent chemical interactions between binary components in the NaCl–Ga 2 S 3 system. In this unique occurrence, previously intact binary crystalline species transform upon melting into mixed liquid structural isomers, forming bonds with new partners. The chemical combinatorics appears to be fully reversible for stable crystals and liquids. Despite this, rapidly frozen glasses out of thermodynamic equilibrium remain in a metastable isomeric state, offering remarkable properties, particularly a high room‐temperature Na + conductivity, comparable to the best sodium halide superionic conductors and therefore encouraging for sodium solid‐state batteries and energy applications. A rigidity paradigm is responsible for the observed phenomenon, as the extremely constrained Ga 2 S 3 crystal lattice does not survive viscous flow, breaking up at a short‐range level. The removal of rigidity constraints and dense packing leads to a significant increase in empty space, which is the origin of high sodium diffusivity. Broadly, the rigidity‐driven structural isomerism opens up an inspiring path to the discovery of atypical materials.

25 ENERGY STORAGE↗

DOE OSTI2024

Chain rigidity controlled aggregation ability and solid-state microstructures for efficient stretchable conjugated polymer films

Stretchable conjugated polymer films with good electrical performance under mechanical deformation are highly desirable for soft electronics. However, the mechanical and electrical properties of these films, particularly in conjugated polymer:elastomer blends, are not fully understood at molecular level. Here, this study explores the relationships among molecular structure, aggregation ability, film microstructure, and the electrical/mechanical properties of three diketopyrrolopyrrole-based conjugated polymers (P1, P2, P3) with decreasing backbone rigidity and their corresponding polymer:elastomer blends. The most flexible polymer P3 shows strong aggregation, which forms highly crystalline fibers to produce fragile neat film and produces large isolated crystallites restricting charge transport in blend film. As chain rigidity increases, the P1 and P2 polymers show weaker aggregation, and produce smaller crystallites in neat films with enhanced ductility. P1 and P2 based blend films display nanocrystallites polymer networks with dispersed elastomer domains. As a result, we achieved near-constant charge mobility before and after stretching under 50 % strain for P2-based blend films with well-controlled pathways for both charge transport and energy dissipation. This study demonstrates the critical role of backbone rigidity in regulating the properties of stretchable conjugated polymer films, paving the way for more reliable and deformable materials in soft electronics.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A Novel Approach for Computing Rigid Body Motion Using Linear Accelerations

Here, a novel approach is presented for computing general rigid body motion based on a few known linear accelerations. This method utilizes linear acceleration data obtained from three distinct points on the body, all within a body-fixed reference frame. The only requirement is that the three chosen points must not be collinear. A system of differential-algebraic equations is derived, combining principles of rigid body kinematics with theory of the rotation group SO(3). These equations provide a framework for numerically computing various motion parameters, including angular velocity, angular acceleration, body orientation, velocity field, acceleration field, and displacement field. By numerically solving this system of equations, we can fully characterize rigid body motion in three-dimensional space. A numerical example is provided to demonstrate the practical implementation and efficacy of the proposed technique, illustrating its potential for accurate motion computation in various applications.

42 ENGINEERING↗

NASA NTRS2021

Development of an SE(3)-based Rigid Body Pose Estimation Scheme for Unknown Moments of Inertia in a Spacecraft

In real-world applications, the consideration of state and parameter uncertainties is an important part of any navigation and control system. Uncertainties can arise because of the instruments, communication systems, or external disturbances. Parameter uncertainty can be due to uncertainties in the data or the calibration process used. The objective of this research is to develop a rigid body pose estimation scheme on nonlinear manifolds of rigid body motion groups for unknown mass properties moments of inertia with application in space launch. An unscented Kalman filter is developed on special Euclidean space and their tangent bundle to address uncertainties in the states and inertia properties. This estimator accounts for uncertainties, while considering rotational-translational coupling, and avoids singularity or non-uniqueness issues. Since this estimator is based on the nonlinear manifolds on which rigid body motion evolves, it is reliable and is expected to result in high level of accuracy. The estimators are validated on a generic model of Logistic Module (LM) and a cuboid spacecraft model. The algorithms can then be tested on Dragon XL, HTV-X, and possibly other spacecraft.

Moments of Inertia↗

DOE OSTI2025

Inertial collapse of a gas bubble in a shear flow near a rigid wall

Despite the extensive research on bubble collapse near rigid walls, the bubble collapse dynamics in the presence of shear flow near a rigid wall is poorly understood. We conduct direct simulations of the Navier–Stokes equations to explore the bubble dynamics and pressures during bubble collapse near a rigid, flat wall under linear shear flow conditions. We examine the dependence of the bubble collapse morphology and wall pressures on the initial bubble location and shear rate. We find that shear distorts the bubble, generating two re-entrant jets – one developing from the side opposite to the mean flow and the other from the far end toward the wall. Upon impact of the jet on the opposite side of the bubble, water-hammer shocks are produced, which propagate outward and interact with the convoluted bubble shape. The shock stretches the bubble towards the wall, resulting in a closer impact location for the jet originating from the far end compared with the case with no shear flow. The water-hammer pressure location can be approximated as the theoretical distance travelled by a particle initialised at the bubble centre with the corresponding constant shear flow velocity. The maximum wall pressures can thus be predicted by considering the distance between the far jet impingement location and the wall along the wall-normal direction. As the shear rate is increased, the maximum wall pressure increases, although only marginally. We determine the critical initial stand-off distance from the wall at which the bubble morphology is shear dominated, i.e. characterised by converging re-entrant jets.

Bhola, Sahil (ORCID:0000000236766302)↗

DOE OSTI2025

Enhancing Biopolyester Backbone Rigidity with an Asymmetric Furanic Monomer

Biobased furanic polyesters can exhibit performance advantages over petroleum-derived polyesters, primarily due to their rigid furan-containing backbones. Herein, we develop two strategies to polymerize methyl 5-hydroxymethyl furanoate to poly(5-hydroxymethyl furanoate) (PHMF), a furan-based polyester with even greater backbone rigidity than poly(ethylene furanoate). Thermal, spectroscopic, and computational investigations of PHMF alongside analogous furan-based and phenyl-based polyesters suggest that the high furan content of PHMF leads to its high glass transition temperature, slow crystallization kinetics, and low amorphous mobility. Molecular dynamics simulations suggest that while the backbone of PHMF is exceptionally rigid, its amorphous phase is denser than its phenyl analog due to noncovalent interchain interactions. Together, these results highlight how asymmetric furan-based monomers can modulate key properties in biobased polyesters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗