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Relevant bibliographies by topics / Euler vectors

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Academic literature on the topic 'Euler vectors'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Euler vectors"

1

Ko, Nak, Seokki Jeong, Suk-seung Hwang, and Jae-Young Pyun. "Attitude Estimation of Underwater Vehicles Using Field Measurements and Bias Compensation." Sensors 19, no. 2 (2019): 330. http://dx.doi.org/10.3390/s19020330.

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This paper proposes a method of estimating the attitude of an underwater vehicle. The proposed method uses two field measurements, namely, a gravitational field and a magnetic field represented in terms of vectors in three-dimensional space. In many existing methods that convert the measured field vectors into Euler angles, the yaw accuracy is affected by the uncertainty of the gravitational measurement and by the uncertainty of the magnetic field measurement. Additionally, previous methods have used the magnetic field measurement under the assumption that the magnetic field has only a horizon

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2

Garat, Alcides. "Euler observers in geometrodynamics." International Journal of Geometric Methods in Modern Physics 11, no. 06 (2014): 1450060. http://dx.doi.org/10.1142/s0219887814500601.

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Euler observers are a fundamental tool for the study of spacetime evolution. Cauchy surfaces are evolved through the use of hypersurface orthogonal fields and their relationship to coordinate observers, that enable the use of already developed algorithms. In geometrodynamics, new tetrad vectors have been introduced with outstanding simplifying properties. We are going to use these already introduced tetrad vectors in the case where we consider a curved four-dimensional Lorentzian spacetime with the presence of electromagnetic fields. These Einstein–Maxwell geometries will provide the new tetra

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3

Bouchet, André. "Compatible Euler Tours and Supplementary Eulerian Vectors." European Journal of Combinatorics 14, no. 6 (1993): 513–20. http://dx.doi.org/10.1006/eujc.1993.1054.

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Nie, Zhaohu. "On Sha's Secondary Chern–Euler Class." Canadian Mathematical Bulletin 55, no. 3 (2012): 586–96. http://dx.doi.org/10.4153/cmb-2011-089-1.

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AbstractFor a manifold with boundary, the restriction of Chern's transgression form of the Euler curvature form over the boundary is closed. Its cohomology class is called the secondary Chern– Euler class and was used by Sha to formulate a relative Poincaré–Hopf theorem under the condition that the metric on the manifold is locally product near the boundary. We show that the secondary Chern–Euler form is exact away from the outward and inward unit normal vectors of the boundary by explicitly constructing a transgression form. Using Stokes’ theorem, this evaluates the boundary term in Sha's rel

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5

Li, Zhao Kui, and Yan Wang. "A Image Decomposition Method Based on Euler Mapping for Face Recognition." Advanced Materials Research 989-994 (July 2014): 4119–22. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.4119.

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This paper presents a robust but simple image feature representation method, called image decomposition based on Euler mapping (IDEM). IDEM firstly captures the orientation information by implementing arctangent operator for each pixel. Then, the orientation image is decomposed into two mapping images by executing Euler mapping. Each mapping image is normalized using the “z-score” method, and all normalized vectors are concatenated into an augmented feature vector. The dimensionality of the augmented feature vector is reduced by linear discriminant analysis to yield a low-dimensional feature v

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Mao, Ailin, and Zhihan Qian. "Eurasian-Pacific-N. American Plate Motions from Very Long Baseline Interferometry." Symposium - International Astronomical Union 156 (1993): 179–84. http://dx.doi.org/10.1017/s0074180900173164.

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We use the baseline variation rates, which are obtained by the VLBI measuring in the past years (1979. /-1991.1), to estimate the relative motions among Eurasian, Pacific and North American plates. A comparion with the geological-based models has been made. In order to strengthen the VLBI constraints on the Euler vectors, we estimate the velocities of unstable stations in addition to the Euler vectors.

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7

Chen, Yong Sheng, Qun He, Jun Yu Chen, and Hong Bin Ma. "Data Processing of IGS Station in China and Analysis of Crustal Movement of Eurasian Plate." Applied Mechanics and Materials 353-356 (August 2013): 3464–67. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.3464.

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By using all 103 days GPS data of IGS in china, from year 2000 to 2005, the baseline is solved with GSMIT software. With One day's baseline solution as the input data, based on the mathematical floating model of station, the floating velocity of station is solved and the crustal movement is gotten; then, according to Euler theorem of plate movement, the Euler vectors of Chinese mainland is obtained; furthermore, the floating velocity of the station area in Eurasian plate is acquired. The results show that, in ITRF2000 framework, the station floating velocity is similar with what announced by I

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8

Becker, R., and S. Panchanadeeswaran. "Crystal Rotations Represented as Rodrigues Vectors." Textures and Microstructures 10, no. 3 (1989): 167–94. http://dx.doi.org/10.1155/tsm.10.167.

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Rodrigues vectors are explored as a means of representing crystal orientation distributions. Relationships between the Rodrigues vectors and several more commonly utilized representations of rotations are presented. The restrictions which cubic material symmetry imposes on the Rodrigues space are examined and relationships for special equivalent configurations are developed. Common crystal orientation distributions are presented as Rodrigues vectors and compared to the more standard representations in terms of pole figures and Euler angles. Applications of the Rodrigues space for illustrating

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9

Goins, Edray Herber, та Asamoah Nkwanta. "Riordan Matrix Representations of Euler’s Constant γ and Euler’s Number e". International Journal of Combinatorics 2016 (6 листопада 2016): 1–9. http://dx.doi.org/10.1155/2016/8324150.

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10

Giacaglia, G. E. O., and W. Q. Lamas. "On Euler-Lagrange's Equations: A New Approach." TEMA (São Carlos) 21, no. 2 (2020): 359. http://dx.doi.org/10.5540/tema.2020.021.02.359.

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A new formalism is proposed to study the dynamics of mechanical systems composed of N connected rigid bodies, by introducing the concept of $6N$-dimensional composed vectors. The approach is based on previous works by the authors where a complete formalism was developed by means of differential geometry, linear algebra, and dynamical systems usual concepts. This new formalism is a method for the description of mechanical systems as a whole and not as each separate part. Euler-Lagrange's Equations are easily obtained by means of this formalism.

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Dissertations / Theses on the topic "Euler vectors"

1

Njoroge, Mary Wambui. "Is Nubia Plate Rigid? A Geodetic Study of the Relative Motion of Different Cratonic Areas within Africa." Scholar Commons, 2015. http://scholarcommons.usf.edu/etd/6003.

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The Nubia plate is normally considered to be a rigid plate and as such used in the realization of terrestrial reference frame. Gondwana breakup plate reconstruction, the Cameroon volcanic line, seismicity, and the morphology of the Okavango rift zone (ORZ) suggest the presence of internal deformation within the Nubia plate. To test this hypothesis, six different reference frames were developed from the velocity field of three individual regions (West, Central and South), and of different combinations of them (West+Central, South+Central, and Nubia as a whole). The residual velocities with resp

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2

Guragac, Hami Sercan. "Equivariant Vector Fields On Three Dimensional Representation Spheres." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613781/index.pdf.

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Let G be a finite group and V be an orthogonal four-dimensional real representation space of G where the action of G is non-free. We give necessary and sufficient conditions for the existence of a G-equivariant vector field on the representation sphere of V in the cases G is the dihedral group, the generalized quaternion group and the semidihedral group in terms of decomposition of V into irreducible representations. In the case G is abelian, where the solution is already known, we give a more elementary solution.

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Neto, Aurelio Menegon. "Números de Milnor e obstrução de Euler." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-14092007-101056/.

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Neste trabalho, definimos a obstrução local de Euler de um espaço analítico complexo singular (X, \'x IND.0\'), denotada por Eu(X, \'x IND.0\'), e a obstrução local de Euler de uma função holomorfa f definida neste espaço, com uma singularidade isolada em \'x IND. 0\', denotada por \'Eu IND. f\' (X, \'x IND.0\'); e apresentamos duas fórmulas para seus respectivos cálculos. Em seguida, através de uma abordagem geométrica, determinamos as relações entre \'Eu IND. f\' (X,\'x IND.0\') e algumas generalizações do número de Milnor para funções em espaços singulares<br>In this work we define the loca

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4

Barbosa, Alex Melges [UNESP]. "Classes de Stiefel-Whitney e de Euler." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/148923.

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Submitted by Alex Melges Barbosa (alex.melgesb@gmail.com) on 2017-03-02T15:41:01Z No. of bitstreams: 1 PDF_final_cd - Alex.pdf: 1031527 bytes, checksum: d71a279fd3f7c761ebeb48e598e07b22 (MD5)<br>Approved for entry into archive by LUIZA DE MENEZES ROMANETTO (luizamenezes@reitoria.unesp.br) on 2017-03-08T13:52:00Z (GMT) No. of bitstreams: 1 barbosa_am_me_sjrp.pdf: 1031527 bytes, checksum: d71a279fd3f7c761ebeb48e598e07b22 (MD5)<br>Made available in DSpace on 2017-03-08T13:52:00Z (GMT). No. of bitstreams: 1 barbosa_am_me_sjrp.pdf: 1031527 bytes, checksum: d71a279fd3f7c761ebeb48e598e07b22 (MD5)

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Siyahhan, Bercan. "A Two Dimensional Euler Flow Solver On Adaptive Cartesian Grids." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609482/index.pdf.

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In the thesis work, a code to solve the two dimensional compressible Euler equations for external flows around arbitrary geometries have been developed. A Cartesianmesh generator is incorporated to the solver. Hence the pre-processing can be performed together with the solution within a single code. The code is written in the C++ programming language and its object oriented capabilities have been exploited to save memory in the data structure developed. The Cartesian mesh is formed by dividing squares successively into its four quadrants. The main advantage of using this type of a mesh is the

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Silva, Mauro Viegas da [UNESP]. "Os teoremas de índice de Poincaré." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/94366.

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Made available in DSpace on 2014-06-11T19:27:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-03-01Bitstream added on 2014-06-13T20:27:38Z : No. of bitstreams: 1 silva_mv_me_rcla.pdf: 927964 bytes, checksum: 1bf8757069fd7950b3ef35b7c13da6ba (MD5)<br>O objetivo deste trabalho é apresentar uma demonstração combinatória dos teore- mas de Índice de Poincaré, a saber: Sejam D um disco e γ seu bordo. Seja V um campo vetorial contínuo sobre D com pontos críticos isolados P1, P2, . . . , Pn pertencentes ao interior de D. Se V nunca se anula em γ, então W(γ) = I(P1) + I(P2) + . . . + I(Pn),

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Krinshnamurthy, R. "Kinetic Flux Vector Splitting Method On Moving Grids (KFMG) For Unsteady Aerodynamics And Aeroelasticity." Thesis, Indian Institute of Science, 2001. http://hdl.handle.net/2005/288.

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Analysis of unsteady flows is a very challenging topic of research. A decade ago, potential flow equations were used to predict unsteady pressures on oscillating bodies. Recognising the fact that nonlinear aerodynamics is essential to analyse unsteady flows accurately, particularly in transonic and supersonic flows, different Euler formulations operating on moving grids have emerged recently as important CFD tools for unsteady aerodynamics. Numerical solution of Euler equations on moving grids based on upwind schemes such as the ones due to van Leer and Roe have been developed for the purpose

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Silva, Mauro Viegas da. "Os teoremas de índice de Poincaré /." Rio Claro : [s.n.], 2011. http://hdl.handle.net/11449/94366.

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Orientador: Alice Kimie Miwa Libardi<br>Banca: Suzinei Aparecida Siqueira Marconato<br>Banca: Karina Schiabel Silva<br>Resumo: O objetivo deste trabalho é apresentar uma demonstração combinatória dos teore- mas de Índice de Poincaré, a saber: "Sejam D um disco e γ seu bordo. Seja V um campo vetorial contínuo sobre D com pontos críticos isolados P1, P2, . . . , Pn pertencentes ao interior de D. Se V nunca se anula em γ, então W(γ) = I(P1) + I(P2) + . . . + I(Pn), onde I(Pi) é o índice do ponto crítico Pi e W(γ) o número de voltas de V sobre γ." "Seja V um campo vetorial tangente contínuo sobre

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9

Silva, Tharsis Souza. "Campos descontínuos com chaveamento no Rn." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/6144.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-09T12:27:04Z No. of bitstreams: 2 Tese - Tharsis Souza Silva - 2016.pdf: 3242823 bytes, checksum: 4cdf7de6c7ba7cfe6f4fc07cc9501592 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-09T12:27:26Z (GMT) No. of bitstreams: 2 Tese - Tharsis Souza Silva - 2016.pdf: 3242823 bytes, checksum: 4cdf7de6c7ba7cfe6f4fc07cc9501592 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made available in DSpace o

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Magot, Jean-Mathieu. "Invariants homotopiques de champs de vecteurs en dimension 3." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM070/document.

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En 1998, R. Gompf a défini un invariant homotopique des champs de plans orientés des 3-variétés fermées orientées. Cet invariant est défini pour les champs de plans orientés xi; de toute 3-variété fermée orientée M dont la première classe de Chern c_1(xi) est un élément de torsion de H_2(M;Z). Dans le premier chapitre de la thèse, nous définissons une extension de l’invariant de Gompf pour toutes les 3-variétés compactes orientées à bord et nous étudions ses variations lors de chirurgies lagrangiennes. Il en résulte que l’invariant de Gompf étendu peut être vu comme un invariant de type fini d

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Books on the topic "Euler vectors"

1

Koppenol, P. J. 3D Euler flow simulations on a Cyber 205 vector computer. National Aerospace Laboratory, 1985.

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2

Anderson, W. Kyle. A comparison of finite volume flux vector splittings for the Euler equations. AIAA, 1985.

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3

Lui, Shiu-Hong. Entropy analysis of kinetic flux vector splitting schemes for the compressible Euler equations. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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4

Isett, Philip. The Divergence Equation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0006.

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This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a smooth function and a smooth vector field on ³, plus an unknown, symmetric (2, 0) tensor. The chapter presents a proposition that takes into account a condition relating to the conservation of momentum as well as a condition that reflects Newton's law, which states that every action must have an equal and opposite reaction. This axiom, in turn, implies the conservation of momentum in classical mechan

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5

Entropy analysis of kinetic flux vector splitting schemes for the compressible Euler equations. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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6

van, Leer Bram, and United States. National Aeronautics and Space Administration., eds. Numerical flux formulas for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1991.

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7

Rajeev, S. G. Hamiltonian Systems Based on a Lie Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0010.

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There is a remarkable analogy between Euler’s equations for a rigid body and his equations for an ideal fluid. The unifying idea is that of a Lie algebra with an inner product, which is not invariant, on it. The concepts of a vector space, Lie algebra, and inner product are reviewed. A hamiltonian dynamical system is derived from each metric Lie algebra. The Virasoro algebra (famous in string theory) is shown to lead to the KdV equation; and in a limiting case, to the Burgers equation for shocks. A hamiltonian formalism for two-dimensional Euler equations is then developed in detail. A discret

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8

Isett, Philip. Basic Technical Outline. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0003.

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This chapter provides a more technical outline of the construction, starting with a solution to the Euler-Reynolds system and a correction v₁ = v + V, p₁ = p + P. The correction V is a divergence free vector field which oscillates rapidly compared to v. In the construction, there will always be a bounded number of waves Vsubscript I (at most 192) which are nonzero at any given time t. Each individual wave Vsubscript I composing V is a complex-valued, divergence free vector field that oscillates rapidly in only one direction. The chapter introduces several ways in which to represent each Vsubsc

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Mann, Peter. Constrained Hamiltonian Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0021.

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This chapter focuses on autonomous geometrical mechanics, using the language of symplectic geometry. It discusses manifolds (including Kähler manifolds, Riemannian manifolds and Poisson manifolds), tangent bundles, cotangent bundles, vector fields, the Poincaré–Cartan 1-form and Darboux’s theorem. It covers symplectic transforms, the Marsden–Weinstein symplectic quotient, presymplectic and symplectic 2-forms, almost symplectic structures, symplectic leaves and foliation. It also discusses contact structures, musical isomorphisms and Arnold’s theorem, as well as integral invariants, Nambu struc

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Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator

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Book chapters on the topic "Euler vectors"

1

Brasselet, Jean-Paul, José Seade, and Tatsuo Suwa. "The Local Euler Obstruction." In Vector fields on Singular Varieties. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05205-7_8.

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van Leer, Bram. "Flux-Vector Splitting for the Euler Equation." In Upwind and High-Resolution Schemes. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60543-7_5.

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Koppenol, P. J. "Simulating 3D Euler Flows on a CYBER 205 Vector Computer." In The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics. Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-663-13912-6_5.

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Rizzi, Arthur, and J. P. Therre. "Vector Algorithm for Large-Memory CYBER 205 Simulations of Euler Flows." In The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics. Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-663-13912-6_6.

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Mandal, J. C., and S. M. Deshpande. "Higher Order Accurate Kinetic Flux Vector Splitting Method for Euler Equations." In Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Vieweg+Teubner Verlag, 1989. http://dx.doi.org/10.1007/978-3-322-87869-4_39.

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Turkel, Eli, and Bram Van Leer. "Flux vector splitting and Runge-Kutta methods for the Euler equations." In Ninth International Conference on Numerical Methods in Fluid Dynamics. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/3-540-13917-6_200.

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Borrel, M., J. L. Montagne, M. Neron, J. P. Veuillot, and A. M. Vuillot. "Implementation of 3D Explicit Euler Codes on a CRAY-1S Vector Computer." In The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics. Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-663-13912-6_3.

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Yin, Zhifeng, and Xinfeng Ge. "The Difference Method of 2-Dimensional Euler Equations With Flux Vector Splitting." In Lecture Notes in Electrical Engineering. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-2185-6_58.

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Jain, R. K., N. Kroll, and R. Radespiel. "Development of Efficient Algorithms for the Solutions of Full Potential and Euler Equations on Vector Computers." In The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics. Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-663-13912-6_2.

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Eberle, Albrecht. "A Nonlinear Flux Vector Split Defect Correction Scheme for Fast Solutions of the Euler and Navier-Stokes Equations." In Hyperbolic Problems: Theory, Numerics, Applications. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8370-2_34.

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Conference papers on the topic "Euler vectors"

1

Kim, Sung-Soo, Bongcheol Seo, and Myungho Kim. "A Study on Mixed Kinetic-Kinematic Equations for Multibody Systems." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12574.

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In this paper, mixed kinetic-kinematic equations for a multibody system have been studied in order to resolve the difficulties of non-integrability of angular velocity vectors. As for the kinetic equations, the Newton-Euler equations of motion are considered. They are derived in terms of angular velocity and angular acceleration vectors expressed in the body fixed reference frames. As for the kinematic compatibility equations, two different equations are considered. One is from the relationship between the angular velocity vector and the time derivatives of Euler parameters. The other is from

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2

Rathod, Cheta M., and Ahmed A. Shabana. "Rail Geometry and Euler Angles." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-13965.

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In railroad vehicle dynamics, Euler angles are often used to describe the track geometry (track centerline and rail space curves). The tangent and curvature vectors as well as local geometric properties such as the curvature and torsion can be expressed in terms of Euler angles. Some of the local geometric properties and Euler angles can be related to measured parameters that are often used to define the track geometry. The Euler angles employed, however, define a coordinate system that may differ from the Frenet frame used in the classical differential geometry. The relationship between the t

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Farooq, Umar, and Brian F. Feeny. "An Experimental Investigation of State-Variable Modal Decomposition Method for Modal Analysis." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87060.

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This work presents the experimental evaluation of the statevariable modal decomposition (SVMD) method for modal parameter estimation of multi degree-of-freedom (MDOF) vibration systems. Using output response ensembles only, the generalized eigenvalue problem is formed to estimate eigen frequencies and modal vectors for a lightly damped linear clamped-free experimental Euler beam. The estimated frequencies and modal vectors are compared against the theoretical system frequencies and modal vectors. Satisfactory results are obtained for estimating both system frequencies and modal vectors for the

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Nachbagauer, Karin, Peter G. Gruber, Yury Vetyukov, and Johannes Gerstmayr. "A Spatial Thin Beam Finite Element Based on the Absolute Nodal Coordinate Formulation Without Singularities." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47732.

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A three-dimensional nonlinear finite element for thin beams is proposed within the absolute nodal coordinate formulation (ANCF). The deformation of the element is described by means of displacement vector, axial slope and axial rotation parameter per node. The element is based on the Bernoulli-Euler theory and can undergo coupled axial extension, bending and torsion in the large deformation case. Singularities — which are typically caused by such parameterizations — are overcome by a director per element node. Once the directors are properly defined, a cross sectional frame is defined at any p

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Fan, W., and W. D. Zhu. "An Accurate Singularity-Free Formulation of a Three-Dimensional Curved Euler-Bernoulli Beam for Flexible Multibody Dynamic Analysis." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60277.

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An accurate singularity-free formulation of a three-dimensional curved Euler-Bernoulli beam with large deformations and large rotations is developed for flexible multibody dynamic analysis. Euler parameters are used to characterize orientations of cross-sections of the beam, which can resolve the singularity problem caused by Euler angles. The position of the centroid line of the beam is integrated from its slope, and position vectors of nodes of beam elements are no longer used as generalized coordinates. Hence, the number of generalized coordinates for each node is minimized. Euler parameter

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Hwang, Yunn-Lin. "Recursive Method for the Dynamic Analysis of Open-Loop Flexible Multibody Systems." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48368.

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Abstract:

The main objective of this paper is to develop a recursive method for the dynamic analysis of open-loop flexible multibody systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve for t

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Phillips, Jeffrey D., Misac N. Nabighian, David V. Smith, and Yaoguo Li. "Estimating locations and total magnetization vectors of compact magnetic sources from scalar, vector, or tensor magnetic measurements through combined Helbig and Euler analysis." In SEG Technical Program Expanded Abstracts 2007. Society of Exploration Geophysicists, 2007. http://dx.doi.org/10.1190/1.2792526.

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Bauchau, Olivier A., and Jou-Young Choi. "The Vectorial Parameterization of Motion." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48304.

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This paper presents a vectorial parameterization of motion that generalizes the vectorial parameterization of rotation. The Pl¨ucker coordinates of an arbitrary material line of a rigid body subjected to a screw motion are shown to transform by the action of a motion tensor. The proposed vectorial parameterization completely describes an arbitrary motion by means of two vectors that constitute an eigenvector of the motion tensor associated with its positive unit eigenvalue. The first vector is conveniently selected as the vectorial parameterization of rotation, and the second is related to the

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Yang, Guolai, James Yang, Chen Qiang, Jianli Ge, and Qiang Chen. "Dynamic Responses of Beam With Sloping Support Traversed by a Moving Mass." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28143.

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This paper contributes to investigation on vibration analysis for cradle subjected to the moving barrel. The tipping part of the gun is simplified by a beam with sloping support traversed by a moving mass. The cradle structure is modeled by Euler-Bernoulli variable cross-section beam and the elevating strut is modeled by elastic supporting rod. The beam and supporting rod are discretized into finite elements, and then the main mass matrix, stiffness matrix, and damping matrix can be formulated. Gravity and inertial force are described by external nodal load vectors. The time-varying additional

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Brodsky, Vladimir, and Moshe Shoham. "Explicit Algorithm for Robot Manipulator Dual Dynamics." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dac-4316.

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Abstract Kinematicians have used dual numbers to obtain rigid body kinematics in a compact three-dimensional form by substituting dual for real numbers in the equation of rotational motion. No such simple relation, known as ‘principle of transference’, existed however, for dynamics. The commonly used inertia binor by which dual momentum is calculated, raises the dual dynamic equations to six dimensions. In fact, the inertia binor does not act on the dual vector as a whole, but rather on its real and dual parts as two distinct real vectors. The recently introduced dual mass operator can serve a

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