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

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NASA NTRS2012

Minimal Coordinate Formulation of Contact Dynamics in Operational Space

In recent years, complementarity techniques have been developed for modeling non-smooth contact and collision dynamics problems for multi-link robotic systems. Normally, in this approach, a linear complementarity problem (LCP) is set up using 6n non-minimal coordinates for a system with n links together with all the unilateral constraints and inter-link bilateral constraints on the system. In this paper, we use operational space dynamics to develop a complementarity formulation for contact and collision dynamics that uses minimal coordinates. The use of such non-redundant coordinates results in much smaller size LCP problems and the automatic enforcement of the inter-link bilateral constraints. Furthermore, we exploit operational space low-order computational algorithms to overcome some of the bottlenecks in using minimal coordinates.

contact dynamics↗

DOE OSTI2026

Multibody for Everybody (M4E) - A Linearization Approach to Enable Frequency Domain Analysis, Time Integration and Control Co-Design

1.1 Background/Objectives: Marine energy represents a promising yet underexploited source of power. To increase the harvested power, significant efforts have been made to improve wave energy converter (WEC) modeling capabilities and optimize power take-off (PTO) performance; however, these efforts have often treated WEC dynamics, PTO design, and controller development sequentially. In contrast, control co-design (CCD) is emerging as a promising strategy to address these issues directly, creating a growing need for fast analysis tools suitable for repeated simulation and parametric studies [1]. To support this need, this work presents the Multibody for Everybody (M4E) [2] linearization module, which employs a symbolic toolbox to provide deeper insight of WEC design parameters. The objective is to demonstrate that a minimal-coordinate linearization of articulated WEC dynamics can provide accurate wave response predictions and substantial computational savings relative to nonlinear time-domain simulation, while preserving compatibility with broader wave-energy analysis workflows, enabling CCD. 1.2 Approach/Activities: The proposed approach linearizes the equations of motion, generated by M4E, in minimal coordinates about a selected operating point and combines the resulting system with frequencydomain hydrodynamic terms to incorporate the reduced mass, damping, stiffness, and forcing operators. The linearized model is used for both impedance-based response amplitude operator (RAO) prediction and rapid regular-wave time integration. The methodology is demonstrated on a single-flap device and a FOSWEC configuration, with linearized M4E responses compared against the corresponding nonlinear M4E simulations and WEC-Sim results. Regular-wave time histories, RAO trends, and runtime differences are assessed. The framework is also compatible with broader wave-energy workflows, including coupling to WecOptTool, although that capability is not the focus of this work [3]. 1.3 Results/Lessons: The linearized M4E model reproduces key regularwave response characteristics such as integration and Response Amplitude over multiple frequencies. This module matches nonlinear M4E and WEC-Sim results while substantially reducing integration cost. Thus, the proposed framework can serve as a rapid analysis layer for articulated WEC design, parameter studies, and controls-oriented workflows. The analysis is most appropriate in the near-equilibrium regime, about the linearization point.

16 TIDAL AND WAVE POWER↗

DOE OSTI2026

SuperLab 2.0 Showcase: Connecting Five Labs to Tackle Grid Complexity and Unlock Unique Grid Asset Potential

SuperLab 2.0 (5-Lab Demo) is a collaborative, national-scale experiment showcasing the coordination of geographically distributed energy assets in real time. The demonstration integrates 25 physical and digital assets, spanning wind, PV, batteries, electrolyzers, DC fast chargers, microgrid controllers, building automation systems, small modular reactor (SMR), control centers, and gas turbines, across five DOE national laboratories-NLR, INL, NETL, LBNL, and SNL. These assets are unified using Energy Sciences Network (ESnet), a low-latency, high-performance U.S. Department of Energy's (DOE) network, and controlled via a centralized energy controller hosted at NLR's ARIES facility. The demonstration validates the ability to stress-test hybrid energy systems under dynamic scenarios to de-risk advanced control strategies for greater resilience and flexibility. SuperLab 2.0 (5-Lab Demo) showcased a major advancement in federated national laboratory collaboration, enabling real-time, cross-laboratory experimentation to coordinate geographically dispersed distributed energy resources (DERs) using various communication protocols and networks. SuperLab 2.0 (5-Lab Demo) built on previous demonstrations conducted between NLR-PNNL and NLR-INL connecting diverse assets including distant protection devices, a SMR simulator, and a high temperature electrolyzer (HTE). Previous demos were based on a single connection between two labs with minimal coordination challenges. The 5-Lab demo with a centralized controller, distributed testbeds across different geographical locations, and use of protocols-based communication represents a scenario closer to real-world grid operations that coordinate resources across a region to meet system needs. This experiment studied how local DER controllers interact with a centralized energy controller during normal and abnormal events to maintain reliability. The SuperLab team across the five labs implemented a notional power system model equivalent of transmission and distribution lines, represented by the data networks interconnecting the labs. Each lab continuously exchanged local parameters (such as P and Q) from its Hardware-In-Loop (CHIL) and Power Hardware-In-Loop (PHIL) assets through centralized energy controller at NLR, enabling real-time interaction and coordination across sites. By leveraging ESnet as the communication backbone, the team successfully operated the distributed assets as a unified power system, with each bus represented by a different laboratory. This setup mirrors how assets interact in real-world power systems across dispersed locations with various protocols and latencies. At each lab site, assets were operated using their own local controllers which were coordinated through an overarching operation and control layer of centralized energy controller, equivalent to how an energy management system (EMS) orchestrates assets across a regional or national grid. SuperLab's federated connectivity utilized a Digital Real-Time Simulators (DRTS)-type gateway to connect Controller Hardware-In-Loop (CHIL) and PHIL assets between labs. To enable this federated connection through ESnet, a deterministic network was established where latency variations were consistent. This consistency allowed the development of digital filters for the power system assets across CHIL and PHIL interfaces to avoid unstable and unreliable grid conditions. This report provides an overview of the cross-laboratory configuration and offers insights into interconnecting geographically distributed research assets to test them as if they were co-located. This experiment represents a step toward linking nine DOE national laboratories, enabling nation-wide simulations that can address utility-driven challenges with grid resilience, flexibility, and modernization.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

The tier system: a host development framework for bioengineering

Development of microorganisms into mature bioproduction host strains has typically been a slow and circuitous process, wherein multiple groups apply disparate approaches with minimal coordination over decades. To help organize and streamline host development efforts, we introduce the Tier System for Host Development, a conceptual model and guide for developing microbial hosts that can ultimately lead to a systematic, standardized, less expensive, and more rapid workflow. The Tier System is made up of three Tiers, each consisting of a unique set of strain development Targets, including experimental tools, strain properties, experimental information, and process models. By introducing the Tier System, we hope to improve host development activities through standardization and systematization pertaining to nontraditional chassis organisms.

09 BIOMASS FUELS↗

NASA NTRS1972

Coordinate transformation by minimizing correlations between parameters

This investigation was to determine the transformation parameters (three rotations, three translations and a scale factor) between two Cartesian coordinate systems from sets of coordinates given in both systems. The objective was the determination of well separated transformation parameters with reduced correlations between each other, a problem especially relevant when the sets of coordinates are not well distributed. The above objective is achieved by preliminarily determining the three rotational parameters and the scale factor from the respective direction cosines and chord distances (these being independent of the translation parameters) between the common points, and then computing all the seven parameters from a solution in which the rotations and the scale factor are entered as weighted constraints according to their variances and covariances obtained in the preliminary solutions. Numerical tests involving two geodetic reference systems were performed to evaluate the effectiveness of this approach.

Kumar, M.↗

NASA NTRS1989

Efficient grid generation

Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a mapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs.

Seki, Rycichi↗

DOE OSTI2020

Understanding the Charging Flexibility of Shared Automated Electric Vehicle Fleets

The combined anticipated trends of vehicle sharing (ride-hailing), automated control, and powertrain electrification are poised to disrupt the current paradigm of predominately owner-driven gasoline vehicles with low levels of utilization. Shared, automated, electric vehicle (SAEV) fleets offer the potential for lower cost and emissions and have garnered significant interest among the research community. While promising, unmanaged operation of these fleets may lead to unintended negative consequences. One potentially unintended consequence is a high quantity of SAEVs charging during peak demand hours on the electric grid, potentially increasing the required generation capacity. This research explores the flexibility associated with charging loads demanded by SAEV fleets in response to servicing personal mobility travel demands. Travel demand is synthesized in four major United States metropolitan areas: Detroit, MI; Austin, TX; Washington, DC; and Miami, FL. In each of these four cities, SAEV simulations are performed using local projected electricity prices from the Regional Energy Deployment System (ReEDS) for a handful of supply side scenarios. A coordinated charging model is introduced that seeks to reduce fleet charging costs in response to time-varying electricity prices and increasing shares of personal trip demand served (between 1% and 25% of all metro trips served by the SAEV fleet). Simulation results are presented across various scenarios assuming fleetwide coordination to minimize charging energy costs while constrained by offering adequate mobility service to fleet customers. The results indicate that the SAEV charging load is highly flexible; energy costs were shown to reduce between 13% and 46% across a wide range of simulated scenarios. In addition, these savings were realized without detrimentally impacting the fleet’s ability to service trips.

autonomous vehicle↗

NASA NTRS2011

Ndarts

Ndarts software provides algorithms for computing quantities associated with the dynamics of articulated, rigid-link, multibody systems. It is designed as a general-purpose dynamics library that can be used for the modeling of robotic platforms, space vehicles, molecular dynamics, and other such applications. The architecture and algorithms in Ndarts are based on the Spatial Operator Algebra (SOA) theory for computational multibody and robot dynamics developed at JPL. It uses minimal, internal coordinate models. The algorithms are low-order, recursive scatter/ gather algorithms. In comparison with the earlier Darts++ software, this version has a more general and cleaner design needed to support a larger class of computational dynamics needs. It includes a frames infrastructure, allows algorithms to operate on subgraphs of the system, and implements lazy and deferred computation for better efficiency. Dynamics modeling modules such as Ndarts are core building blocks of control and simulation software for space, robotic, mechanism, bio-molecular, and material systems modeling.

Jain, Abhinandan↗

NASA NTRS2016

Global Precipitation Measurement (GPM) and International Space Station (ISS) Coordination for CubeSat Deployments to Minimize Collision Risk

The Global Precipitation Measurement Mission (GPM) is a joint U.S. and Japan mission to observe global precipitation, extending the Tropical Rainfall Measuring Mission (TRMM), which was launched by H-IIA from Tanegashima in Japan on February 28TH, 2014 directly into its 407km operational orbit. The International Space Station (ISS) is an international human research facility operated jointly by Russia and the USA from NASA's Johnson Space Center (JSC) in Houston Texas. Mission priorities lowered the operating altitude of ISS from 415km to 400km in early 2105, effectively placing both vehicles into the same orbital regime. The ISS has begun a program of deployments of cost effective CubeSats from the ISS that allow testing and validation of new technologies. With a major new asset flying at the same effective altitude as the ISS, CubeSat deployments became a serious threat to GPM and therefore a significant indirect threat to the ISS. This paper describes the specific problem of collision threat to GPM and risk to ISS CubeSat deployment and the process that was implemented to keep both missions safe from collision and maximize their project goals.

Pawloski, James H.↗

NASA NTRS2018

Global Precipitation Measurement (GPM) Core Satellite & International Space Station (ISS) Coordination for CubeSat Deployments to Minimize Collision Risk

The Global Precipitation Measurement Mission (GPM) is a joint U.S. and Japan mission to observe global precipitation, extending the Tropical Rainfall Measuring Mission (TRMM) data set, which was launched by H-IIA from Tanegashima in Japan on February 28TH, 2014 directly into its 407km operational orbit. The International Space Station (ISS) is an international human research facility operated jointly by Russia and the USA from NASA's Johnson Space Center (JSC) in Houston Texas. Mission priorities lowered the operating altitude of ISS from 415km to 400km in early 2015, effectively placing both vehicles into the same orbital regime. The ISS has begun a program of deployments of cost effective CubeSats from the ISS that allow testing and validation of new technologies. With a major NASA asset flying at the same effective altitude as the ISS, CubeSat deployments became a serious threat to GPM and therefore a significant indirect threat to the ISS. This presentation describes the specific problem of collision threat to GPM and risk to ISS CubeSat deployment, the process that was implemented to keep both missions safe from collision and maximize their project goals, and the history of the process since implementation.

GPM↗

NASA NTRS1974

Coordinate systems for the space shuttle program

A minimal set of well defined coordinate systems necessary for the interchange of data within the space shuttle program is presented. The document format consists of four parts: (1) a list of the subscripts identifying the coordinate systems, (2) a glossary explaning the terms used within the coordinate system definitions, (3) figures defining, both graphically and verbally, each coordinate system, and (4) an appendix (published separately) showing the relationships (transformations) between similar systems.

Davis, L. D.↗

NASA NTRS2005

Metronome Use for Coordination of Breaths and Cardiac Compressions Delivered by Minimally-Trained Caregivers During Two-Person CPR

Astronaut crew medical officers (CMO) aboard the International Space Station (ISS) receive 40 hours of medical training over 18 months before each mission, including two-person cardiopulmonary resuscitation (2CPR) as recommended by the American Heart Association (AHA). Recent studies have concluded that the use of metronomic tones improves the coordination of 2CPR by trained clinicians. 2CPR performance data for minimally-trained caregivers has been limited. The goal of this study was to determine whether use of a metronome by minimally-trained caregivers (CMO analogues) would improve 2CPR performance. 20 pairs of minimally-trained caregivers certified in 2CPR via AHA guidelines performed 2CPR for 4 minutes on an instrumented manikin using 3 interventions: 1) Standard 2CPR without a metronome [NONE], 2) Standard 2CPR plus a metronome for coordinating compression rate only [MET], 3) Standard 2CPR plus a metronome for coordinating both the compression rate and ventilation rate [BOTH]. Caregivers were evaluated for their ability to meet the AHA guideline of 32 breaths-240 compressions in 4 minutes. All (100%) caregivers using the BOTH intervention provided the required number of ventilation breaths as compared with the NONE caregivers (10%) and MET caregivers (0%). For compressions, 97.5% of the BOTH caregivers were not successful in meeting the AHA compression guideline; however, an average of 238 compressions of the desired 240 were completed. None of the caregivers were successful in meeting the compression guideline using the NONE and MET interventions. This study demonstrates that use of metronomic tones by minimally-trained caregivers for coordinating both compressions and breaths improves 2CPR performance. Meeting the breath guideline is important to minimize air entering the stomach, thus decreasing the likelihood of gastric aspiration. These results suggest that manifesting a metronome for the ISS may augment the performance of 2CPR on orbit and thus may increase the level of care.

Hurst, Victor, IV↗

DOE OSTI2023

ORNL_AISD_NiPt

This dataset describes the nickel-platinum (NiPt) solid solution binary alloy, where the two constituent elements nickel (Ni) and platinum (Pt) are randomly placed on the face centered cubic (FCC) crystal structure, with the lattice constant of 3.840 angstroms. The dataset comprises data for three different sizes of the crystal structure: 256 atoms, 864 atoms, and 2,048 atoms, each of which contains 1900 configurations. For each size of the crystal structure, the data set was generated for concentrations ranging from 0at% of Pt to 100at% of Pt in the NiPt binary system, with increasing the concentration of Pt in the system every 5at%. For each one of the chemical compositions, 100 random configurations were generated, each with a different random seed. Each of the output files contains the mass, type, atomic coordinates, energy per atom, and forces in x, y, and z directions respectively. For each atomic configuration, the output was collected every 150 steps during the minimization stage and every 1000 steps during the replica exchange stage. Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [1], which is a molecular dynamics code, was used to generate data for NiPt alloy. The simulation used the interatomic potential for NiPt binary system MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001 [3] from the OpenKIM library (Open Knowledgebase of Interatomic Models) [2]. This potential was developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM). The simulation process begins with the generation of the random NiPt structure and follows with the short minimization and replica exchange simulation. The minimization procedure adjusts atomic coordinates and performs energy minimization, which typically leads to a local potential energy minimum. The method used for the minimization was the conjugate gradient algorithm. A short replica exchange (parallel tempering) simulation involves four replicas (ensembles) of a system and follows the minimization stage. Multiple snapshots of the configuration were collected during the minimization and replica exchange stages. NiPt alloy is interesting due to its magnetic and charge transfer properties [4]. The data is provided in three compressed zipped folders: atoms256.zip, atoms864.zip, atoms2048.zip Each zipped folder contains the data that describes crystals of size 256 atoms, 864 atoms, and 2,048 atoms respectively. Each one of the three zipped folders contains the data structured in the following way: -Ni_ground_state.cfg --> atomic configuration for the pure nickel -Pt_ground_state.cfg --> atomic configuration for the pure platinum -Pt#_filtered --> folders containing atomic configurations for #at% concentration of platinum. The folder contains 100 atomic configurations, each saved in a subfolder. Each subfolder named config* is associated with a specific atomic configuration. Each of these subfolders contains files with .cfg format, corresponding to outputs for each atomic configuration The total number of atomic configurations contained in atoms256.zip is 65,046. The total number of atomic configurations contained in atoms864.zip is 63,936. The total number of atomic configurations contained in atoms2048.zip is 61,997. The total number of atomic configurations spanned by the entire dataset is 190,979. References [1] https://www.lammps.org/ [2] https://openkim.org/ [3] https://openkim.org/id/MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001 [4] El-Gendy, Ahmed A. and Hampel, Silke and Büccchner, Bernd and Klingeler, Rüdiger, Tuneable magnetic properties of carbon-shielded NiPt-nanoalloys, RSC Adv., volume 6, issue 57, pages 52427-52433, 2016, The Royal Society of Chemistry, doi:10.1039/C6RA05910D

36 MATERIALS SCIENCE↗

DOE OSTI2023

ORNL_AISD_NiPt_108atoms

This dataset describes the nickel-platinum (NiPt) solid solution binary alloy, where the two constituent elements nickel (Ni) and platinum (Pt) are randomly placed on the face centered cubic (FCC) crystal structure, with the lattice constant of 3.840 angstroms. The dataset comprises data for crystal structures with 108 atoms with 1,900 configurations. The data set was generated for concentrations ranging from 0at% of Pt to 100at% of Pt in the NiPt binary system, with increasing the concentration of Pt in the system every 5at%. For each one of the chemical compositions, 100 random configurations were generated, each with a different random seed. Each of the output files contains the mass, type, atomic coordinates, energy per atom, and forces in x, y, and z directions respectively. For each atomic configuration, the output was collected every 150 steps during the minimization stage and every 1000 steps during the replica exchange stage. Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [1], which is a molecular dynamics code, was used to generate data for NiPt alloy. The simulation used the interatomic potential for NiPt binary system 'MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001' [3] from the OpenKIM library (Open Knowledgebase of Interatomic Models) [2]. This potential was developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM). The simulation process begins with the generation of the random NiPt structure and follows with the short minimization and replica exchange simulation. The minimization procedure adjusts atomic coordinates and performs energy minimization, which typically leads to a local potential energy minimum. The method used for the minimization was the conjugate gradient algorithm. A short replica exchange (parallel tempering) simulation involves four replicas (ensembles) of a system and follows the minimization stage. Multiple snapshots of the configuration were collected during the minimization and replica exchange stages. NiPt alloy is interesting due to its magnetic and charge transfer properties [4]. The data is provided in a compressed zipped folders atoms108.zip. The zipped folder contains the data structured in the following way: - Ni_ground_state.cfg --> atomic configuration for the pure nickel - Pt_ground_state.cfg --> atomic configuration for the pure platinum - Pt#_filtered --> folders containing atomic configurations for #at% concentration of platinum. The folder contains 100 atomic configurations, each saved in a subfolder - Each subfolder named config* is associated with a specific atomic configuration. Each of these subfolders contains files with .cfg format, corresponding to outputs for each atomic configuration The total number of atomic configurations contained in atoms108.zip is 66,132. This dataset is an extension to the dataset ORNL_AISD_NiPt [5] that has been previously released with crystal structures of 256 atoms, 864 atoms, and 2,048 atoms, with the same methodology for data collection. References [1] https://www.lammps.org/ [2] https://openkim.org/ [3] https://openkim.org/id/MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001 [4] El-Gendy, Ahmed A. and Hampel, Silke and BÃ¼chner, Bernd and Klingeler, RÃ¼diger, Tuneable magnetic properties of carbon-shielded NiPt-nanoalloys, RSC Adv., volume 6, issue 57, pages 52427-52433, 2016, The Royal Society of Chemistry, doi:10.1039/C6RA05910D [5] M. Karabin, M. Lupo Pasini, and M. Eisenbach. ORNL_AISD_NiPt. United States: N. p., 2023. Web. doi:10.13139/OLCF/1958172.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Evidence of Completion of Milestone 3: Experimental Testbed

Construction and deployment of the experimental testbed encountered scheduling delays, and completion was subsequently further delayed by curtailment of LANL operations due to the COVID-19 pandemic. Between March and October, LANL was in a state of “Limited Operations” such that only certain “mission-critical” work was performed with approximately 25% on-site staffing. In spite of this, much of the lab space preparation was executed and the five initial model house” units were constructed and installed during this period. Still, the pace of construction was impacted by difficulty in coordinating personnel and minimizing contact between workers. Currently, LANL is in the mode of “Normal Operations with Maximum Telework,” which continues to limit the availability of on-site personnel. Nevertheless, Milestone 3 is now complete. This document describes the experiment as it is deployed and provides status for each task for this milestone.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2021

Evidence of Completion of Milestone 3: Experimental Testbed

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1990

Multiple Access Trade Study

The Personal Access Satellite System (PASS) strawman design uses a hybrid Time Division Multiple Access (TDMA)/Frequency Division Multiple Access (FDMA) implementation. TDMA is used for the forward direction (from Suppliers to Users), and FDMA for the return direction (from Users to Suppliers). An alternative architecture is proposed that will require minimal real time coordination and yet provide a fast access method by using random access Code Division Multiple Access (CDMA). The CDMA system issues are addressed such as connecting suppliers and users, both of whom may be located anywhere in the CONUS, when the user terminals are constrained in size and weight; and providing efficient traffic routing under highly variable traffic requirements. It is assumed that bandwidth efficiency is not of paramount importance. CDMA or Spread Spectrum Multiple Access (SSMA) communication is a method in which a group of carriers operate at the same nominal center frequency but are separable from each other by the low cross correlation of the spreading codes used. Interference and multipath rejection capability, ease of selective addressing and message screening, low density power spectra for signal hiding and security, and high resolution ranging are among the benefits of spread spectrum communications.

Motamedi, Masoud↗

NASA NTRS1993

Nonrecursive formulations of multibody dynamics and concurrent multiprocessing

Since the late 1980's, research in recursive formulations of multibody dynamics has flourished. Historically, much of this research can be traced to applications of low dimensionality in mechanism and vehicle dynamics. Indeed, there is little doubt that recursive order N methods are the method of choice for this class of systems. This approach has the advantage that a minimal number of coordinates are utilized, parallelism can be induced for certain system topologies, and the method is of order N computational cost for systems of N rigid bodies. Despite the fact that many authors have dismissed redundant coordinate formulations as being of order N(exp 3), and hence less attractive than recursive formulations, we present recent research that demonstrates that at least three distinct classes of redundant, nonrecursive multibody formulations consistently achieve order N computational cost for systems of rigid and/or flexible bodies. These formulations are as follows: (1) the preconditioned range space formulation; (2) penalty methods; and (3) augmented Lagrangian methods for nonlinear multibody dynamics. The first method can be traced to its foundation in equality constrained quadratic optimization, while the last two methods have been studied extensively in the context of coercive variational boundary value problems in computational mechanics. Until recently, however, they have not been investigated in the context of multibody simulation, and present theoretical questions unique to nonlinear dynamics. All of these nonrecursive methods have additional advantages with respect to recursive order N methods: (1) the formalisms retain the highly desirable order N computational cost; (2) the techniques are amenable to concurrent simulation strategies; (3) the approaches do not depend upon system topology to induce concurrency; and (4) the methods can be derived to balance the computational load automatically on concurrent multiprocessors. In addition to the presentation of the fundamental formulations, this paper presents new theoretical results regarding the rate of convergence of order N constraint stabilization schemes associated with the newly introduced class of methods.

Kurdila, Andrew J.↗