SEARCH · Search NASA

Results for “phase change memory”

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.

SourceResearch connectionFrom yearThrough year

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

At least 55 records · Page 3

All sources NASA NTRS DOE OSTI

NASA NTRSDate not supplied

Influence of Microstructural Features on Austenite-Martensite Interfaces in NiTi Shape Memory Alloys

Shape memory alloys (SMAs) exhibit several unique thermomechanical properties due to a reversible martensitic phase transformation. A key aspect of this transformation is the austenite-martensite interface. Here we present a molecular dynamics (MD) simulation methodology to study the atomic-scale features of austenite-martensite interface migration under near-equilibrium conditions. In single crystals, the interfaces migrate rapidly with only a small thermodynamic driving force. In polycrystals, however, interface migration is significantly impeded due to the change in orientation relationship at grain boundaries and the stored elastic energy resulting from microstructural constraints. This behavior can be linked to several mechanisms associated with transformation width and hysteresis in SMAs, properties of great importance for applications involving actuation. Additionally, we will present preliminary MD simulation results on the influence of precipitates on the formation and migration of austenite-martensite interfaces.

Gabriel Plummer↗

NASA NTRS2014

Assessment of Shape Memory Alloys - From Atoms To Actuators - Via In Situ Neutron Diffraction

As shape memory alloys (SMAs) become an established actuator technology, it is important to identify the fundamental mechanisms responsible for their performance by understanding microstructure performance relationships from processing to final form. Yet, microstructural examination of SMAs at stress and temperature is often a challenge since structural changes occur with stress and temperature and microstructures cannot be preserved through quenching or after stress removal, as would be the case for conventional materials. One solution to this dilemma is in situ neutron diffraction, which has been applied to the investigation of SMAs and has offered a unique approach to reveal the fundamental micromechanics and microstructural aspects of bulk SMAs in a non-destructive setting. Through this technique, it is possible to directly correlate the micromechanical responses (e.g., internal residual stresses, lattice strains), microstructural evolutions (e.g., texture, defects) and phase transformation properties (e.g., phase fractions, kinetics) to the macroscopic actuator behavior. In this work, in situ neutron diffraction was systematically employed to evaluate the deformation and transformation behavior of SMAs under typical actuator conditions. Austenite and martensite phases, yield behavior, variant selection and transformation temperatures were characterized for a polycrystalline NiTi (49.9 at. Ni). As the alloy transforms under thermomechanical loading, the measured textures and lattice plane-level variations were directly related to the cyclic actuation-strain characteristics and the dimensional instability (strain ratcheting) commonly observed in this alloy. The effect of training on the shape memory characteristics of the alloy and the development of two-way shape memory effect (TWSME) were also assessed. The final conversion from a material to a useful actuator, typically termed shape setting, was also investigated in situ during constrained heatingcooling and subsequent shape recovery experiments. Neutron diffraction techniques are also being applied to the investigation of novel high temperature SMAs with the objective of designing alloys with better stability, higher transition temperatures and ultimately superior durability.

Shape Memory Alloys↗

NASA NTRS2005

Properties and Potential of Two (ni,pt)ti Alloys for Use as High-temperature Actuator Materials

The microstructure, transformation temperatures, basic tensile properties, shape memory behavior, and work output for two (Ni,Ti)Pt high-temperature shape memory alloys have been characterized. One was a Ni30Pt20Ti50 alloy (referred to as 20Pt) with transformation temperatures above 230 C and the other was a Ni20Pt30Ti50 alloy (30Pt) with transformation temperatures about 530 C. Both materials displayed shape memory behavior and were capable of 100% (no-load) strain recovery for strain levels up to their fracture limit (3-4%) when deformed at room temperature. For the 20Pt alloy, the tensile strength, modulus, and ductility dramatically increased when the material was tested just about the austenite finish (A(sub f)) temperature. For the 30Pt alloy, a similar change in yield behavior at temperatures above the A(sub f) was not observed. In this case the strength of the austentite phase was at best comparable and generally much weaker than the martensite phase. A ductility minimum was also observed just below the A(sub s) temperature in this alloy. As a result of these differences in tensile behavior, the two alloys performed completely different when thermally cycled under constant load. The 20Pt alloy behaved similar to conventional binary NiTi alloys with work output due to the martensite-to-austenite transformation initially increasing with applied stress. The maximum work output measured in the 20Pt alloy was nearly 9 J/cu cm and was limited by the tensile ductility of the material. In contrast, the martensite-to-austenite transformation in the 30Pt alloy was not capable of performing work against any bias load. The reason for this behavior was traced back to its basic mechanical properties, where the yield strength of the austenite phase was similar to or lower than that of the martensite phase, depending on temperature. Hence, the recovery or transformation strain for the 30Pt alloy under load was essentially zero, resulting in zero work output.

Noebe, Ronald↗

NASA NTRS2010

Phase Transformation and Creep Behavior in Ti50Pd30Ni20 High Temperature Shape Memory Alloy in Compression

The creep behavior and the phase transformation of Ti50Pd30Ni20 High Temperature Shape Memory Alloy (HTSMA) is investigated by standard creep tests and thermomechanical tests. Ingots of the alloy are induction melted, extruded at high temperature, from which cylindrical specimens are cut and surface polished. A custom high temperature test setup is assembled to conduct the thermomechanical tests. Following preliminary monotonic tests, standard creep tests and thermally induced phase transformation tests are conducted on the specimen. The creep test results suggest that over the operating temperatures and stresses of this alloy, the microstructural mechanisms responsible for creep change. At lower stresses and temperatures, the primary creep mechanism is a mixture of dislocation glide and dislocation creep. As the stress and temperature increase, the mechanism shifts to predominantly dislocation creep. If the operational stress or temperature is raised even further, the mechanism shifts to diffusion creep. The thermally induced phase transformation tests show that actuator performance can be affected by rate independent irrecoverable strain (transformation induced plasticity + retained martensite) as well as creep. The rate of heating and cooling can adversely impact the actuators performance. While the rate independent irrecoverable strain is readily apparent early in the actuators life, viscoplastic strain continues to accumulate over the lifespan of the HTSMA. Thus, in order to get full actuation out of the HTSMA, the heating and cooling rates must be sufficiently high enough to avoid creep.

Kumar, Parikshith K.↗

NASA NTRS1979

The effect of accuracy, conservation and filtering on numerical weather forecasting

Considerations leading to the numerical design of the GLAS fourth-order global atmospheric model are discussed, including changes recently introduced into the model. The computation time and memory requirements for the fourth-order model are similar to those of the present second-order GLAS model with the same 4 deg latitude, 5 deg longitude, and 9 vertical-level resolution. However, the fourth-order model forecast skill is significantly better than that of the current GLAS model, and after three days it is comparable to the 2.5 by 3 deg version of the GLAS model in the sea level pressure maps, and has less phase errors in the 500 mb maps.

Kalnay-Rivas, E.↗

NASA NTRS2016

LS3MIP (v1.0) Contribution to CMIP6: The Land Surface, Snow and Soil Moisture Model Intercomparison Project Aims, Setup and Expected Outcome.

The Land Surface, Snow and Soil Moisture Model Intercomparison Project (LS3MIP) is designed to provide a comprehensive assessment of land surface, snow, and soil moisture feedbacks on climate variability and climate change, and to diagnose systematic biases in the land modules of current Earth System Models (ESMs). The solid and liquid water stored at the land surface has a large influence on the regional climate, its variability and predictability, including effects on the energy, water and carbon cycles. Notably, snow and soil moisture affect surface radiation and flux partitioning properties, moisture storage and land surface memory. They both strongly affect atmospheric conditions, in particular surface air temperature and precipitation, but also large-scale circulation patterns. However, models show divergent responses and representations of these feedbacks as well as systematic biases in the underlying processes. LS3MIP will provide the means to quantify the associated uncertainties and better constrain climate change projections, which is of particular interest for highly vulnerable regions (densely populated areas, agricultural regions, the Arctic, semi-arid and other sensitive terrestrial ecosystems).The experiments are subdivided in two components, the first addressing systematic land biases in offline mode (LMIP, building upon the 3rd phase of Global Soil Wetness Project; GSWP3) and the second addressing land feedbacks attributed to soil moisture and snow in an integrated framework (LFMIP, building upon the GLACE-CMIP blueprint).

atmospheric temperature↗

NASA NTRS2014

Using SpF to Achieve Petascale for Legacy Pseudospectral Applications

Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community. We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. Highlevel abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical kernels that can be performed entirely inprocessor. The granularity of domain decomposition provided by SpF is only constrained by the datalocality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures. In this presentation, we will describe our experience in porting legacy pseudospectral models, MoSST and DYNAMO, to use SpF as well as present preliminary performance results provided by the improved scalability.

DYNAMO↗

NASA NTRS2013

SpF: Enabling Petascale Performance for Pseudospectral Dynamo Models

Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community.We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. High-level abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical kernels that can be performed entirely in-processor. The granularity of domain-decomposition provided by SpF is only constrained by the data-locality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures.In this presentation, we will describe the basic architecture of SpF as well as preliminary performance data and experience with adapting legacy dynamo codes. We will conclude with a discussion of planned extensions to SpF that will provide pseudospectral applications with additional flexibility with regard to time integration, linear solvers, and discretization in the radial direction.

Pseudospectral (PS)↗

NASA NTRS2016

NiTi Alloys for Tribological Applications: The Role of In-Situ Nanotechnology

Beginning in 2004, NASA initiated the investigation and development of, Nitinol 60, a nickel-rich and dimensionally stable version of shape memory alloy Nitinol 55, as an alternative to bearing steel. Early investigations showed it to be hard and impervious to aqueous corrosion but the fundamental reasons for these properties were unknown. Shape memory alloys made from equiatomic Ni-Ti are widely known for their unique dimensional instability behavior that can be triggered by thermal and mechanical stress. The nickel-rich alloys exhibit no such dimension change property and have high hardness but have largely been overlooked by industry and the engineering community. Though steel is the dominant material of choice for mechanical components (bearings and gears) it has intrinsic limitations related to corrosion and plastic deformation. In contrast, Ni-Ti alloys are intrinsically rustproof and can withstand high contact loads without damage (denting). Over the last decade, focused RD to exploit these alloys for new applications has revealed that in-situ nano-scale phases that form during processing are largely responsible for NiTis remarkable properties. In this presentation, the state-of-art of nickel-rich NiTi alloys will be introduced and the nanotechnology behind their intriguing behavior will be addressed. The presentation will include discussion of how NASA is adopting this new technology inside the space station water recycling system as a pathfinder for more down-to-earth tribological challenges.

metals↗

NASA NTRS1988

PSA: A program to streamline orbit determination for launch support operations

An interactive, menu driven computer program was written to streamline the orbit determination process during the critical launch support phase of a mission. Residing on a virtual memory minicomputer, this program retains the quantities in-core needed to obtain a least squares estimate of the spacecraft trajectory with interactive displays to assist in rapid radio metric data evaluation. Menu-driven displays allow real time filter and data strategy development. Graphical and tabular displays can be sent to a laser printer for analysis without exiting the program. Products generated by this program feed back to the main orbit determination program in order to further refine the estimate of the trajectory. The final estimate provides a spacecraft ephemeris which is transmitted to the mission control center and used for antenna pointing and frequency predict generation by the Deep Space Network. The development and implementation process of this program differs from that used for most other navigation software by allowing the users to check important operating features during development and have changes made as needed.

Legerton, V. N.↗

NASA NTRS2017

Precipitation Strengthenable NiTiPd High Temperature Shape Memory Alloys

In binary NiTi alloys, it has long been known that Ni-rich alloys can be heat treated to produce precipitates which both strengthen the matrix against dislocations and improve the behavior of the material under thermal and mechanical cycling. Within recent years, the same effect has been observed in Ni-rich NiTiHf high temperature shape memory alloys and heat treatment regimens have been defined which will reliably produce improved properties. In NiTiPd alloys, precipitation has also been observed, but studies are still underway to define reliable heat treatments and compositions which will provide a balance of strengthening and good thermomechanical properties. For this study, a series of NiTi-32 at.Pd alloys was produced to determine the effect of changing nickeltitanium content on the transformation behavior and heat treatability of the material. Samples were aged at temperatures between 350C and 450C for times up to 100 hours. Actuation type behavior was evaluated using uniaxial constant force thermal cycling (UCFTC) to determine the effect of composition and aging on the material behavior. TEMSEM was used to evaluate the microstructure and determine the types of precipitates formed. The correlation between composition, heat treat, microstructure, and thermomechanical behavior will be addressed and discussed.

Transformation strain↗

NASA NTRS2010

Fast-Response-Time Shape-Memory-Effect Foam Actuators

Bulk shape memory alloys, such as Nitinol or CuAlZn, display strong recovery forces undergoing a phase transformation after being strained in their martensitic state. These recovery forces are used for actuation. As the phase transformation is thermally driven, the response time of the actuation can be slow, as the heat must be passively inserted or removed from the alloy. Shape memory alloy TiNi torque tubes have been investigated for at least 20 years and have demonstrated high actuation forces [3,000 in.-lb (approximately equal to 340 N-m) torques] and are very lightweight. However, they are not easy to attach to existing structures. Adhesives will fail in shear at low-torque loads and the TiNi is not weldable, so that mechanical crimp fits have been generally used. These are not reliable, especially in vibratory environments. The TiNi is also slow to heat up, as it can only be heated indirectly using heater and cooling must be done passively. This has restricted their use to on-off actuators where cycle times of approximately one minute is acceptable. Self-propagating high-temperature synthesis (SHS) has been used in the past to make porous TiNi metal foams. Shape Change Technologies has been able to train SHS derived TiNi to exhibit the shape memory effect. As it is an open-celled material, fast response times were observed when the material was heated using hot and cold fluids. A methodology was developed to make the open-celled porous TiNi foams as a tube with integrated hexagonal ends, which then becomes a torsional actuator with fast response times. Under processing developed independently, researchers were able to verify torques of 84 in.-lb (approximately equal to 9.5 Nm) using an actuator weighing 1.3 oz (approximately equal to 37 g) with very fast (less than 1/16th of a second) initial response times when hot and cold fluids were used to facilitate heat transfer. Integrated structural connections were added as part of the net shape process, eliminating the need for welding, adhesives, or mechanical crimping. Inexpensive net-shape processing was used, which reduces the cost of the actuator by over a factor of 10 over nonporous TiNi made by hot drawing of tube or electrical discharge machining. By forming the alloy as an open-celled foam, the surface area for heat transfer is dramatically increased, allowing for much faster response times. The technology also allows for netshape fabrication of the actuator, which allows for structural connections to be integrated into the actuator material, making these actuators significantly less expensive. Commercial applications include actuators for concepts such as the variable area chevron and nozzle in jet aircraft. Lightweight tube or rod components can be supplied to interested parties.

Jardine, Peter↗

NASA NTRSDate not supplied

Towards Accurate Predictions of Martensitic Transition Temperatures for Shape Memory Alloys from Ab Initio Simulations

Experimentally, NiTi undergoes a single martensitic phase transition around 341 K from the lowtemperature (T) monoclinic B19’ phase (P21/m) to the high-temperature cubic B2 phase (Pm3m). Theoretically, an orthorhombic B33 (Cmcm) has also been proposed as the T=0 ground state structure, although this phase has never been observed. Accurate predictions of martensitic transition temperatures (MTT) have remained elusive in part due to several well-known theoretical complexities of these systems including low temperature instabilities of the B2 phase. Recently, we proposed a rigorous thermodynamic integration approach based on ab initio simulations to resolve many of these difficulties [1,2]. However, an unsatisfying overprediction of the MTT relative to experiment (by ~100 K) means a fully quantitative theory is still lacking. In this work, we report several new developments to our method that bring first principles theory and experiment much closer into agreement. Our calculations indicate that phonon free energies at low temperature stabilizes B19’ over B33, rationalizing B19’ as the ground state down to T=0. We also find that accurate computations of the electronic free energy, i.e. the change in energy and the appearance of electronic configurational entropy due to finite temperature, is crucial to obtain accurate MTT. Incorporating these corrections results in an MTT prediction of 365 K for binary NiTi, which is in very close agreement with experiment. Our theoretical approach is expected to be a broadly applicable and predictive theory for MTT of SMAs.

Zhigang Wu↗

NASA NTRS2010

Compact Ku-Band T/R Module for High-Resolution Radar Imaging of Cold Land Processes

Global measurement of terrestrial snow cover is critical to two of the NASA Earth Science focus areas: (1) climate variability and change and (2) water and energy cycle. For radar backscatter measurements, Ku-band frequencies, scattered mainly within the volume of the snowpack, are most suitable for the SWE (snow-water equivalent) measurements. To isolate the complex effects of different snowpack (density and snowgrain size), and underlying soil properties and to distinctly determine SWE, the space-based synthetic aperture radar (SAR) system will require a dual-frequency (13.4 and 17.2 GHz) and dual polarization approach. A transmit/receive (T/R) module was developed operating at Ku-band frequencies to enable the use of active electronic scanning phased-array antenna for wide-swath, high-resolution SAR imaging of terrestrial snow cover. The T/R module has an integrated calibrator, which compensates for all environmental- and time-related changes, and results in very stable power and amplitude characteristics. The module was designed to operate over the full frequency range of 13 to 18 GHz, although only the two frequencies, 13.4 GHz and 17.2 GHz, will be used in this SAR radar application. Each channel of the transmit module produces > 4 W (35 dbm) over the operating bandwidth of 20 MHz. The stability requirements of <0.1 dB receive gain accuracy and <0.1 dB transmit power accuracy over a wide temperature range are achieved using a self-correction scheme, which does real-time amplitude calibration so that the module characteristics are continually corrected. All the calibration circuits are within the T/R module. The timing and calibration sequence is stored in a control FPGA (field-programmable gate array) while an internal 128K 8bit high-speed RAM (random access memory) stores all the calibration values. The module was designed using advanced components and packaging techniques to achieve integration of the electronics in a 2 x6.5x1-in. (5x17x2.5-cm) package. The module size allows 4 T/R modules to feed the 16 16-element subarray on an antenna panel. The T/R module contains four transmit channels and eight receive channels (horizontal and vertical polarizations).

Andricos, Constantine↗

NASA NTRS2024

Molecular Dynamics Simulations of Microstructural Effects on Austenite-Martensite Interfaces in NiTi

Formation and migration of austenite-martensite interfaces plays the key role in reversible martensitic transformations of shape memory alloys (SMAs). How these interfaces interact with the SMA microstructure is a primary determining factor in important functional properties such as hysteresis and transformation span. As such, successful microstructural engineering of SMAs requires in-depth knowledge of interface behavior. The rapid nature of martensitic transformations makes experimental observations of moving austenite-martensite interfaces challenging. Molecular dynamics (MD) simulation is a unique tool which can probe the atomic-scale details of austenite-martensite interfaces as they migrate through different microstructures. However, in focusing on the entire transformation process, including the nucleation of new phases, MD studies are usually performed so far from equilibrium that their relevance to experiment is questionable. Here, we demonstrate new MD techniques to generate energetically preferred austenite-martensite interfaces in NiTi under near-equilibrium conditions. The interfaces are semi-coherent, exhibiting a series of structural disconnections, and they can migrate rapidly through single crystals under only small thermodynamic driving forces. In contrast, when interfaces migrate in polycrystals, their motion is impeded by thermoelastic effects as well as changes in orientation relationships at grain boundaries. Microstructures which accumulate large amounts of elastic energy tend to release some fraction through irreversible, hysteresis-inducing mechanisms. We demonstrate that engineering microstructures with less constraints is a viable strategy to produce SMAs with reduced hysteresis and transformation span. Similar thermoelastic and hysteresis-inducing mechanisms also arise when austenite-martensite interfaces encounter precipitates and can be controlled by tuning characteristics of the precipitate distribution.

Gabriel Plummer↗

NASA NTRSDate not supplied

Molecular Dynamics Simulations of Microstructural Effects on Austenite-Martensite Interfaces in NiTi

The formation and migration of austenite-martensite interfaces plays the key role in reversible martensitic transformations of shape memory alloys (SMAs). How these interfaces interact with the SMA microstructure is a primary determining factor in important functional properties such as hysteresis and transformation span. As such, successful microstructural engineering of SMAs requires in-depth knowledge of interface behavior. The rapid nature of martensitic transformations makes experimental observations of moving austenite-martensite interfaces challenging. Molecular dynamics (MD) simulation is a unique tool which can probe the atomic-scale details of austenite-martensite interfaces as they migrate through different microstructures. However, in focusing on the entire transformation process, including the nucleation of new phases, MD studies are usually performed so far from equilibrium that their relevance to experiment is questionable. Here, we demonstrate new MD techniques to generate energetically preferred austenite-martensite interfaces in NiTi under near-equilibrium conditions. The interfaces are semi-coherent, exhibiting a series of structural disconnections, and they can migrate rapidly through single crystals under only small thermodynamic driving forces. In contrast, when interfaces migrate in polycrystals, their motion is impeded by thermoelastic effects as well as changes in orientation relationships at grain boundaries. Microstructures which accumulate large amounts of elastic energy tend to release some fraction through irreversible, hysteresis-inducing mechanisms. We demonstrate that engineering microstructures with less constraints is a viable strategy to produce SMAs with reduced hysteresis and transformation span. Similar thermoelastic and hysteresis-inducing mechanisms also arise when austenite-martensite interfaces encounter precipitates and can be controlled by tuning characteristics of the precipitate distribution.

Gabriel Plummer↗

NASA NTRSDate not supplied

Molecular Dynamics Simulations of Microstructural Effects on Austenite-Martensite Interfaces in NiTi

Gabriel Plummer↗

NASA NTRS1994

Identification and control of structures in space

During the last phase of the project, emphasis has changed to flexible space robotics, by mutual agreement between Dr. R. C. Montgomery, NASA Technical Officer, and the Principal Investigator. Significant advances have been achieved over the period covered by this report. Research has been concerned with two main subjects: (1) the maneuvering and control of freely floating flexible space robots, and (2) the development of a theory for the motion of flexible multibody systems. Work on the first subject has resulted in two papers, both of them concerned with planar maneuvers. The first is concerned with the maneuvering and delivery of a payload to a certain point and in a certain orientation in space. The second is concerned with the docking maneuver with a target whose motion is not known a priori. Both papers will appear in the 'Journal of Guidance, Control, and Dynamics.' The second subject is concerned with the development of hybrid (ordinary and partial) differential equations for the three dimensional motion of flexible multibody systems, a subject of vital interest in flexible space robotics. The paper will appear in the 'Journal of Guidance, Control and Dynamics' in an issue dedicated to the memory of Lawrence W. Taylor, Jr. Abstracts and copies of the papers are hereby included.

Meirovitch, Leonard↗