Relevant bibliographies by topics / N-body integration

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'N-body integration'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "N-body integration"

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Dehnen, Walter. "Towards time symmetric N-body integration." Monthly Notices of the Royal Astronomical Society 472, no. 1 (August 2, 2017): 1226–38. http://dx.doi.org/10.1093/mnras/stx1944.

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AARSETH, S. "NBODY2: A direct N-body integration code." New Astronomy 6, no. 5 (August 2001): 277–91. http://dx.doi.org/10.1016/s1384-1076(01)00060-4.

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Aarseth, Sverre J. "Direct N-Body Calculations." Symposium - International Astronomical Union 113 (1985): 251–59. http://dx.doi.org/10.1017/s0074180900147424.

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The main principles for direct integration of large point-mass systems are outlined. Most particles are advanced by the Ahmad-Cohen neighbour scheme, using fourth-order force polynomials and individual time-steps. Close encounters and persistent binaries are handled by two-body regularization, whereas extreme triple and quadruple configurations are treated as unperturbed systems by special regularization techniques. As an illustration of these methods, we discuss some recent results of an isolated system containing 1000 particles of unequal mass, with special emphasis on the post-collapse phase.
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Hardy, David J., Daniel I. Okunbor, and Robert D. Skeel. "Symplectic variable step size integration for N-body problems." Applied Numerical Mathematics 29, no. 1 (January 1999): 19–30. http://dx.doi.org/10.1016/s0168-9274(98)00031-2.

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Mikkola, Seppo, and Sverre J. Aarseth. "An efficient integration method for binaries in N-body simulations." New Astronomy 3, no. 5 (July 1998): 309–20. http://dx.doi.org/10.1016/s1384-1076(98)00018-9.

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Daverio, David, Yves Dirian, and Ermis Mitsou. "General relativistic cosmological N-body simulations. Part I. Time integration." Journal of Cosmology and Astroparticle Physics 2019, no. 10 (October 28, 2019): 065. http://dx.doi.org/10.1088/1475-7516/2019/10/065.

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Kearns, Melissa J., William H. Warren, Andrew P. Duchon, and Michael J. Tarr. "Path Integration from Optic Flow and Body Senses in a Homing Task." Perception 31, no. 3 (March 2002): 349–74. http://dx.doi.org/10.1068/p3311.

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We examined the roles of information from optic flow and body senses (eg vestibular and proprioceptive information) for path integration, using a triangle completion task in a virtual environment. In two experiments, the contribution of optic flow was isolated by using a joystick control. Five circular arenas were used for testing: (B) both floor and wall texture; (F) floor texture only, reducing information for rotation; (W) wall texture only, reducing information for translation; (N) a no texture control condition; and (P) an array of posts. The results indicate that humans can use optic flow for path integration and are differentially influenced by rotational and translational flow. In a third experiment, participants actively walked in arenas B, F, and N, so body senses were also available. Performance shifted from a pattern of underturning to overturning and exhibited decreased variability, similar responses with and without optic flow, and no attrition. The results indicate that path integration can be performed by integrating optic flow, but when information from body senses is available it appears to dominate.
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Miller, R. H. "Dimensionality of Stable and Unstable Directions in the Gravitational N—Body Problem." International Astronomical Union Colloquium 172 (1999): 139–47. http://dx.doi.org/10.1017/s0252921100072493.

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AbstractThe gravitational n—body problem is chaotic. Phase trajectories that start very near each other separate rapidly. The rate looks exponential over long times. At any instant, trajectories separated in certain directions move apart rapidly (unstable directions), while those separated in other directions stay about the same (stable directions). Unstable directions lie along eigenvectors that correspond to positive eigenvalues of the matrix of force gradients. The number of positive eigenvalues of that matrix gives the dimensionality of stable regions. This number has been studied numerically in a series of 100—body integrations. It continues to change as long as the integration continues because the matrix changes extremely rapidly. On average, there are about 1.2n unstable directions out of 3n. Issues of dimensionality arise when the tools of ergodic studies are brought to bear on the problem of trajectory separation. A method of estimating the rate of trajectory separation based on matrix descriptions is presented in this note. Severe approximations are required.
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Pal, A., and A. Suli. "Solving linearized equations of the N-body problem using the Lie-integration method." Monthly Notices of the Royal Astronomical Society 381, no. 4 (November 11, 2007): 1515–26. http://dx.doi.org/10.1111/j.1365-2966.2007.12248.x.

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Vlachos, D. S., and T. E. Simos. "Partitioned Linear Multistep Method for Long Term Integration of the N-Body Problem." Applied Numerical Analysis & Computational Mathematics 1, no. 2 (December 2004): 540–46. http://dx.doi.org/10.1002/anac.200410017.

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Dissertations / Theses on the topic "N-body integration"

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Qureshi, Muhammad Amer. "Efficient numerical integration for gravitational N-body simulations." Thesis, University of Auckland, 2012. http://hdl.handle.net/2292/10826.

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Models for N-body gravitational simulations of the Solar System vary from small simulations of two bodies over short intervals of time to simulations of large numbers of bodies over long-term integration. Most simulations require the numerical solution of an initial value problem (IVP) of second-order ordinary differential equation. We present new integration methods intended for accurate simulations that are more efficient than existing methods. In the first part of the thesis, we present new higher-order explicit Runge–Kutta Nyström pairs. These new pairs are searched using a simulated annealing algorithm based on optimisation. The new pairs are up to approximately 60% more efficient than the existing ones. We implement these new pairs for a variety of gravitational problems and investigate the growth of global error in position for these problems along with relative error in conserved quantities. The second part consists of the implementation of the Gauss Implicit Runge-Kutta methods in an efficient way such that the error growth satisfies Brouwer’s Law. Numerical experiments show that using the new way of implementation reduces the integration cost up to 20%. We also implement continuous extensions for the Gauss implicit Runge-Kutta methods, using interpolation polynomials at nodal points.
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Gerlach, Enrico. "Stabilitätsuntersuchungen an Asteroidenbahnen in ausgewählten Bahnresonanzen des Edgeworth-Kuiper-Gürtels." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1225227803732-58854.

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Gegenstand dieser Dissertation ist eine umfassende Analyse der Stabilität von Asteroidenbahnen im Edgeworth-Kuiper-Gürtel am Beispiel der 3:5-, 4:7- und der 1:2-Bahnresonanz mit Neptun. Einen weiteren Schwerpunkt der Arbeit bildet die Untersuchung der numerischen Berechenbarkeit der Lyapunov-Zeit von Asteroidenbahnen. Ausgehend von einer allgemeinen Beschreibung der bei numerischen Berechnungen auftretenden Rundungs- und Diskretisierungsfehler wird deren Wachstum bei numerischen Integrationen ermittelt. Diese, teilweise maschinenabhängigen, Fehler beeinflussen die berechnete Trajektorie des Asteroiden ebenso wie die daraus abgeleitete Lyapunov-Zeit. Durch Beispielrechnungen mit unterschiedlichen Rechnerarchitekturen und Integrationsmethoden wird der Einfluss auf die erhaltenen Lyapunov-Zeiten eingehend untersucht. Als Maß zur Beschreibung dieser Abhängigkeit wird ein Berechenbarkeitsindex $\kappa$ definiert. Weiterhin wird gezeigt, dass die allgemeine Struktur des Phasenraumes robust gegenüber diesen Änderungen ist. Unter Nutzung dieser Erkenntnis werden anschließend ausgewählte Bahnresonanzen im Edgeworth-Kuiper-Gürtel untersucht. Grundlegende Charakteristika, wie die Resonanzbreiten, werden dabei aus einfachen Modellen abgeleitet. Eine möglichst realitätsnahe Beschreibung der Stabilität wird durch numerische Integration einer Vielzahl von Testkörpern zusammen mit den Planeten Jupiter bis Neptun erreicht. Die erhaltenen Ergebnisse werden dabei mit der beobachteten Verteilung der Asteroiden im Edgeworth-Kuiper-Gürtel verglichen. ---- Hinweis: Beim Betrachten der pdf-Version dieses Dokumentes mit dem Acrobat Reader mit einer Version kleiner 8.0 kann es unter Windows zu Problemen in der Darstellung der Abbildungen auf den Seiten 46, 72, 74, 79 und 86 kommen. Um die Datenpunkte zu sehen ist eine Vergrößerung von mehr als 800% notwendig. Alternativ kann in den Grundeinstellungen der Haken für das Glätten von Vektorgraphiken entfernt werden
This dissertation presents a comprehensive description of the stability of asteroid orbits in the Edgeworth-Kuiper belt taking the 3:5, 4:7 and 1:2 mean motion resonance with Neptune as example. Further emphasis is given to the numerical computability of the Lyapunov time of asteroids. Starting with a general description of rounding and approximation errors in numerical computations, the growth of these errors within numerical integrations is estimated. These, partly machine-dependent errors influence the calculated trajectory of the asteroid as well as the derived Lyapunov time. Different hardware architectures and integration methods were used to investigate the influence on the computed Lyapunov time. As a measure of this dependence a computability index $\kappa$ is defined. Furthermore it is shown, that the general structure of phase space is robust against these changes. Subsequently, several selected mean motion resonances in the Edgeworth-Kuiper belt are investigated using these findings. Basic properties, like the resonance width, are deduced from simple models. To get a realistic description of the stability, a huge number of test particles was numerically integrated together with the planets Jupiter to Neptune. The obtained results are compared to the observed distribution of asteroids in the Edgeworth-Kuiper belt. ---- Additional information: If the pdf-file of this document is viewed using Acrobat Reader with a version less 8.0 under Windows the figures on page 46, 72, 74, 79 and 86 are shown incomplete. To see the data points a zoom factor larger than 800% is necessary. Alternatively the smoothing of vector graphics should be disabled in the settings of the reader
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Ferrari, Guilherme Gonçalves. "Novos mapas simpléticos para integração de sistemas hamiltonianos com múltiplas escalas de tempo : enfoque em sistemas gravitacionais de N-corpos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/127985.

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Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan.
Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.
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Book chapters on the topic "N-body integration"

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Sweatman, W. L. "N-Body Integration on a Transputer Array." In Dynamics and Interactions of Galaxies, 219–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75273-5_52.

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Aarseth, Sverre J. "Integration Methods for Small N-Body Systems." In Astrophysics and Space Science Library, 287–307. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2917-3_47.

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Nobili, Anna M. "The Accumulation of Integration Error." In Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, 109–16. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3053-7_7.

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Ferrándiz, José M., M. Eugenia Sansaturio, and Jesús Vigo. "Long-Time Predictions of Satellite Orbits by Numerical Integration." In Predictability, Stability, and Chaos in N-Body Dynamical Systems, 387–94. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4684-5997-5_32.

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Sein-Echaluce, M. L., and J. M. Franco. "A New Radial Intermediary and its Numerical Integration." In Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, 217–22. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3053-7_19.

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Pereira, Nuno Sidónio Andrade. "A Parallel N-Body Integrator Using MPI." In Vector and Parallel Processing – VECPAR’98, 627–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/10703040_47.

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Speck, Robert, Daniel Ruprecht, Rolf Krause, Matthew Emmett, Michael Minion, Mathias Winkel, and Paul Gibbon. "Integrating an N-Body Problem with SDC and PFASST." In Lecture Notes in Computational Science and Engineering, 637–45. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05789-7_61.

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"Numerical Integration of the n-body Equations of Motion." In Orbital Mechanics for Engineering Students, 693–99. Elsevier, 2010. http://dx.doi.org/10.1016/b978-0-12-374778-5.00017-9.

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"Numerical Integration of the n -Body Equations of Motion." In Orbital Mechanics for Engineering Students, 725–31. Elsevier, 2014. http://dx.doi.org/10.1016/b978-0-08-097747-8.15003-0.

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"Numerical integration of the n-body equations of motion." In Orbital Mechanics for Engineering Students, 741–47. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102133-0.09991-8.

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Conference papers on the topic "N-body integration"

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Andreev, V. S., S. V. Goryainov, and A. V. Krasilnikov. "N-body problem solution with composition numerical integration methods." In 2016 XIX IEEE International Conference on Soft Computing and Measurements (SCM). IEEE, 2016. http://dx.doi.org/10.1109/scm.2016.7519726.

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Alesova, Irina M., Levon K. Babadzanjanz, Irina Yu Pototskaya, Yulia Yu Pupysheva, and Artur T. Saakyan. "Taylor series method of numerical integration of the N-body problem." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992354.

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Rajasekharan, B., C. Salm, R. J. E. Hueting, T. Hoang, and J. Schmitz. "Dimensional scaling effects on transport properties of ultrathin body p-i-n diodes." In 2008 9th International Conference on Ultimate Integration on Silicon (ULIS). IEEE, 2008. http://dx.doi.org/10.1109/ulis.2008.4527172.

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Duan, Shanzhong. "A Hybrid Parallelizable Algorithm for Computer Simulation of Rigid Body Molecular Dynamics." In 2007 First International Conference on Integration and Commercialization of Micro and Nanosystems. ASMEDC, 2007. http://dx.doi.org/10.1115/mnc2007-21504.

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Molecular dynamics is effective for a nano-scale phenomenon analysis. This paper presents a hybrid parallelizable algorithm for the computer simulation of the motion behavior of molecular chain and open-tree structure on parallel computing system. The algorithm is developed from an approach of rigid body dynamics, in which interbody constraints are exposed so that a system of largely independent multibody subchains is formed. The increased parallelism is obtainable through bringing interbody constraints to evidence and the explicit determination of the associated constraint forces combined with a sequential O(n) procedure. Each subchain then is assigned to a processor for parallel computing. The algorithm offers a sequential O(n) performance if there is only one processor available. The algorithm has O(log2n) computational efficiency if there are as many processors available as number for molecular bodies. For most common scenario, the algorithm will give a computational complexity between O(n) and O(log2n) if number of available processor is less than number of molecular bodies.
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Blackston, David T., James W. Demmel, Andrew R. Neureuther, and Bo Wu. "Integration of an adaptive parallel N-body solver into a particle-by-particle electron-beam interaction simulator." In SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, edited by Eric Munro. SPIE, 1999. http://dx.doi.org/10.1117/12.370132.

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Duan, Shanzhong, and Andrew Ries. "An Efficient O(N) Algorithm for Computer Simulation of Rigid Body Molecular Dynamics." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42032.

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Molecular dynamics is effective for a nano-scale phenomenon analysis. There are two major computational costs associated with computer simulation of atomistic molecular dynamics. They are calculation of the interaction forces and formation/solution of equations of motion. In this paper, an O(N) (order N) procedure is presented for calculation of the interaction forces and formation/solution of equations of motion. For computational costs associated with potentials or interaction forces, an internal coordinate method is used. Use of the internal coordinate method makes application of multi-rigid body molecular dynamics to an atomistic molecular system become possible. The algorithm based on the method makes the calculation considerably more practical for large-scale problems encountered in molecular dynamics such as conformation dynamics of polymers. For computational costs associated with formation/solution of equations of motion, Kane method and the internal coordinate method are used for recursive formation and solution of equations of motion of an atomistic molecular system. However, in computer simulation of atomistic molecular dynamics, the inclusion of lightly excited all degrees of freedom of an atom, such as inter-atomic oscillations and rotation about double bonds with high frequencies, introduces limitations to the simulation. The high frequencies of these degrees of freedom force the use of very small integration step sizes, which severely limit the time scales for the atomic molecular simulation over long periods of time. To improve this, holonomic constraints such as strictly constant bond lengths and bond angles are introduced to freeze these high frequency degrees of freedom since they have insignificant effect on long time scale processes in conformational dynamics. In this way, the procedure developed in multibody dynamics can be utilized to achieve higher computing efficiency and an O(N) computational performance can be realized for formation/solution of equations of motion.
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Younes, Ahmad Bani, and James D. Turner. "An Analytic Continuation Method to Integrate Constrained Multi-Body Dynamical Systems." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37809.

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Many numerical integration methods have been developed for predicting the evolution of the response of dynamical systems. Standard algorithms approach approximate the solution at a future time by introducing a truncated power series representation that attempts to recover an n-th order Taylor series approximation, while only numerically sampling a single derivative model. This work presents an exact fifth-order analytic continuation method for integrating constrained multi-body vector-valued systems of equations, where the Jacobi form of the Routh-Voss equations of motion simultaneously generates the acceleration and Lagrange multiplier solution. The constraint drift problem is addressed by introducing an analytic continuation method that rigorously enforces the kinematic constraints through five time derivatives. This work rigorously deals with the problem of handling the time-varying matrix equations that characterize real-world equation of motion models arising in science and engineering. The proposed approach is expected to be particularly useful for stiff dynamical systems, as well as systems where implicit integration formulations are introduced. Numerical examples are presented that demonstrate the effectiveness of the proposed methodology.
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Tindell, R. H. "Computational Fluid Dynamic Applications for Jet Propulsion System Integration." In ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/90-gt-343.

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The impact of computational fluid dynamics (CFD) methods on the development of advanced aerospace vehicles is growing stronger year by year. Design engineers are now becoming familiar with CFD tools and are developing productive methods and techniques for their applications. This paper presents and discusses applications of CFD methods used at Grumman to design and predict the performance of propulsion system elements such as inlets and nozzles. The paper demonstrates techniques for applying various CFD codes and shows several interesting and unique results. A novel application of a supersonic Euler analysis of an inlet approach flow field, to clarify a wind tunnel-to-flight data conflict, is presented. In another example, calculations and measurements of low-speed inlet performance at angle of attack are compared. This is highlighted by employing a simplistic and low-cost computational model. More complex inlet flow phenomena at high angles of attack, calculated using an approach that combines a panel method with a Navier-Stokes (N-S) code, is also reviewed. The inlet fluid mechanics picture is rounded out by describing an N-S calculation and a comparison with test data of an offset diffuser having massively separated flow on one wall. Finally, the propulsion integration picture is completed by a discussion of the results of nozzle-afterbody calculations, using both a complete aircraft simulation in a N-S code, and a more economical calculation using an equivalent body of revolution technique.
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Warren, M., and J. Salmon. "An O(NlogN) hypercube N-body integrator." In the third conference. New York, New York, USA: ACM Press, 1988. http://dx.doi.org/10.1145/63047.63051.

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Wehage, R. A. "Solution of Multibody Dynamics Using Natural Factors and Iterative Refinement: Part I — Open Kinematic Loops." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0115.

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Abstract An O(n) methodology employing block matrix partitioning and recursive projection to solve multibody equations of motion coupled by a sparse connectivity matrix was developed in (Wehage 1988, 1989, Wehage and Shabana, 1989). These primitive equations, which include all joint generalized and absolute coordinates and constraint reaction forces, are easily obtained from free body diagrams. The corresponding recursive algorithms isolate the generalized joint accelerations for numerical integration and offer the best computational advantage when solving long kinematic chains on serial processors. Recursion, however, precludes effective exploitation of vector or parallel processors. Therefore this paper explores less recursive algorithms by applying the inverse of joint connectivity to eliminate absolute accelerations and constraint forces yielding a generalized system of equations. The resulting positive definite generalized inertia matrix is first represented symbolically as a product of sparse matrices, of which some are singular and then as the product of nonsingular factors obtained recursively. This algorithm has overhead ranging from O(n2) to O(n) depending on the degree of system parallelism. Incorporating iterative refinement and exploiting parallel and vector processing makes this approach competitive for many applications.
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