Relevant bibliographies by topics / Algebraic point projection

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

Academic literature on the topic 'Algebraic point projection'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 January 2023

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Journal articles on the topic "Algebraic point projection"

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Cheng, Taixia, Zhinan Wu, Xiaowu Li, and Chan Wang. "Point Orthogonal Projection onto a Spatial Algebraic Curve." Mathematics 8, no. 3 (2020): 317. http://dx.doi.org/10.3390/math8030317.

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Point orthogonal projection onto a spatial algebraic curve plays an important role in computer graphics, computer-aided geometric design, etc. We propose an algorithm for point orthogonal projection onto a spatial algebraic curve based on Newton’s steepest gradient descent method and geometric correction method. The purpose of Algorithm 1 in the first step of Algorithm 4 is to let the initial iteration point fall on the spatial algebraic curve completely and successfully. On the basis of ensuring that the iteration point fallen on the spatial algebraic curve, the purpose of the intermediate fo
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Wang, Xudong, Xiaowu Li, and Yuxia Lyu. "Application of Orthogonal Polynomial in Orthogonal Projection of Algebraic Surface." Axioms 11, no. 10 (2022): 544. http://dx.doi.org/10.3390/axioms11100544.

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Point orthogonal projection onto an algebraic surface is a very important topic in computer-aided geometric design and other fields. However, implementing this method is currently extremely challenging and difficult because it is difficult to achieve to desired degree of robustness. Therefore, we construct an orthogonal polynomial, which is the ninth formula, after the inner product of the eighth formula itself. Additionally, we use the Newton iterative method for the iteration. In order to ensure maximum convergence, two techniques are used before the Newton iteration: (1) Newton’s gradient d
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Liao, Huanyu, Pavan Kumar Vaitheeswaran, Tao Song, and Ganesh Subbarayan. "Algebraic Point Projection for Immersed Boundary Analysis on Low Degree NURBS Curves and Surfaces." Algorithms 13, no. 4 (2020): 82. http://dx.doi.org/10.3390/a13040082.

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Point projection is an important geometric need when boundaries described by parametric curves and surfaces are immersed in domains. In problems where an immersed parametric boundary evolves with time as in solidification or fracture analysis, the projection from a point in the domain to the boundary is necessary to determine the interaction of the moving boundary with the underlying domain approximation. Furthermore, during analysis, since the driving force behind interface evolution depends on locally computed curvatures and normals, it is ideal if the parametric entity is not approximated a
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Wu, Zhinan, and Xiaowu Li. "An Improved Curvature Circle Algorithm for Orthogonal Projection onto a Planar Algebraic Curve." Mathematics 7, no. 10 (2019): 912. http://dx.doi.org/10.3390/math7100912.

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Point orthogonal projection onto planar algebraic curve plays an important role in computer graphics, computer aided design, computer aided geometric design and other fields. For the case where the test point p is very far from the planar algebraic curve, we propose an improved curvature circle algorithm to find the footpoint. Concretely, the first step is to repeatedly iterate algorithm (the Newton’s steepest gradient descent method) until the iterated point could fall on the planar algebraic curve. Then seek footpoint by using the algorithm (computing footpoint q ) where the core technology
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Geyer, Wulf-Dieter, Moshe Jarden, and Aharon Razon. "On stabilizers of algebraic function fields of one variable." Advances in Geometry 17, no. 2 (2017): 131–74. http://dx.doi.org/10.1515/advgeom-2016-0026.

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AbstractLet $\tilde K$ be a fixed algebraic closure of an infinite field K. We consider an absolutely integral curve Γ in $\mathbb{P}_{K}^{n}$ with n ≥ 2. The curve $\it\Gamma_{\tilde{K}}$ should have only finitely many inflection points, finitely many double tangents, and there exists no point in $\mathbb{P}_{\tilde{K}}^{n}$ through which infinitely many tangents to $\it\Gamma_{\tilde{K}}$ go. In addition there exists a prime number q such that $\it\Gamma_{\tilde{K}}$ has a cusp of multiplicity q and the multiplicities of all other points of $\it\Gamma_{\tilde{K}}$ are at most q. Under these
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Gibson, C. G., and D. Marsh. "On the Geometry of Geared 5-Bar Motion." Journal of Mechanical Design 112, no. 4 (1990): 620–27. http://dx.doi.org/10.1115/1.2912654.

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A new approach is adopted to study the geometry of the coupler curves associated to geared 5-bar motion. The key idea is to think of a configuration of the mechanism as a point in a higher - dimensional configuration space; the family of all configurations is then represented by an algebraic curve in that space. Coupler curves appear naturally as projections of this curve, so their properties can be deduced by projection, independent of any explicit knowledge of their equations.
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Bagchi, Susmit. "Topological Analysis of Fibrations in Multidimensional (C, R) Space." Symmetry 12, no. 12 (2020): 2049. http://dx.doi.org/10.3390/sym12122049.

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A holomorphically fibred space generates locally trivial bundles with positive dimensional fibers. This paper proposes two varieties of fibrations (compact and non-compact) in the non-uniformly scalable quasinormed topological (C, R) space admitting cylindrically symmetric continuous functions. The projective base space is dense, containing a complex plane, and the corresponding surjective fiber projection on the base space can be fixed at any point on real subspace. The contact category fibers support multiple oriented singularities of piecewise continuous functions within the topological spa
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ARGYROS, IOANNIS K. "ON SOME PROJECTION METHODS FOR APPROXIMATING FIXED POINTS OF NONLINEAR EQUATIONS IN BANACH SPACE." Tamkang Journal of Mathematics 21, no. 4 (1990): 351–57. http://dx.doi.org/10.5556/j.tkjm.21.1990.4682.

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 We use a Newton-like method to approximate a fixed point of a non- linear operator equation in a Banach space. Our iterates are computed at each step by solving a linear algebraic system of finite order. 
 
 
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Bharkhada, Deepak, Hengyong Yu, Hong Liu, Robert Plemmons, and Ge Wang. "Line-Source Based X-Ray Tomography." International Journal of Biomedical Imaging 2009 (2009): 1–8. http://dx.doi.org/10.1155/2009/534516.

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Current computed tomography (CT) scanners, including micro-CT scanners, utilize a point x-ray source. As we target higher and higher spatial resolutions, the reduced x-ray focal spot size limits the temporal and contrast resolutions achievable. To overcome this limitation, in this paper we propose to use a line-shaped x-ray source so that many more photons can be generated, given a data acquisition interval. In reference to the simultaneous algebraic reconstruction technique (SART) algorithm for image reconstruction from projection data generated by an x-ray point source, here we develop a gen
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Bidnichenko, Helena. "FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 100 (May 24, 2021): 37–46. http://dx.doi.org/10.32347/0131-579x.2021.100.37-46.

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The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection.
 It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image durin
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Dissertations / Theses on the topic "Algebraic point projection"

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Shelestunova, Veronika. "Infinite Sets of D-integral Points on Projective Algebrain Varieties." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1192.

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Let <em>X</em>(<em>K</em>) &sub; <strong>P</strong><sup><em>n</em></sup> (<em>K</em>) be a projective algebraic variety over <em>K</em>, and let <em>D</em> be a subset of <strong>P</strong><sup><em>n</em></sup><sub><em>OK</em></sub> such that the codimension of <em>D</em> with respect to <em>X</em> &sub; <strong>P</strong><sup><em>n</em></sup><sub><em>OK</em></sub> is two. We are interested in points <em>P</em> on <em>X</em>(<em>K</em>) with the property that the intersection of the closure of <em>P</em> and <em>D</em> is empty in <strong>P</strong><sup><em>n</em></sup><sub><em>OK</em></sub>
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Dokchan, Rakporn. "Numerical integration of differential-algebraic equations with harmless critical points." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16318.

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Algebro-Differentialgleichungen (engl. differential-algebraic equations - DAEs) sind implizite singuläre gewöhnliche Differentialgleichungen, die restringierte dynamische Prozesse beschreiben. Sie unterscheiden sich von expliziten gewöhnlichen Differentialgleichungen dahingehend, dass Anfangswerte nicht beliebig vorgegeben werden können. Weiterhin sind in einer DAE neben Integrations- auch Differentiationsaufgaben involviert. Der Differentiationsindex gibt an, wieviele Differentiationen zur Lösung notwendig sind. Seit den 1980er Jahren wird vorwiegend an der Charakterisierung und Klassifizi
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Shaddad, Amna. "The classification and dynamics of the momentum polytopes of the SU(3) action on points in the complex projective plane with an application to point vortices." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/the-classification-and-dynamics-of-the-momentum-polytopes-of-the-su3-action-on-points-in-the-complex-projective-plane-with-an-application-to-point-vortices(456a7a49-ef1b-4660-a8e6-8d4cd0791d9d).html.

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We have fully classified the momentum polytopes of the SU(3) action on CP(2)xCP(2) and CP(2)xCP(2) xCP(2), both actions with weighted symplectic forms, and their corresponding transition momentum polytopes. For CP(2)xCP(2) the momentum polytopes are distinct line segments. The action on CP(2)xCP(2) xCP(2), has 9 different momentum polytopes. The vertices of the momentum polytopes of the SU(3) action on CP(2)xCP(2) xCP(2), fall into two categories: definite and indefinite vertices. The reduced space corresponding to momentum map image values at definite vertices is isomorphic to the 2-sphere. W
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(9435722), Pavankumar Vaitheeswaran. "Interface Balance Laws, Growth Conditions and Explicit Interface Modeling Using Algebraic Level Sets for Multiphase Solids with Inhomogeneous Surface Stress." Thesis, 2020.

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Interface balance laws are derived to describe transport across a phase interface. This is used to derive generalized conditions for phase nucleation and growth, valid even for solids with inhomogeneous surface stress.<div><br></div><div>An explicit interface tracking approach called Enriched Isogeometric Analysis (EIGA) is used to simulate phase evolution. Algebraic level sets are used as a measure of distance and for point projection, both necessary operations in EIGA. Algebraic level sets are observed to often fail for surfaces. Rectification measures are developed to make algebraic level s
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Books on the topic "Algebraic point projection"

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Dolgachev, I. Point sets in projective spaces and theta functions. Société mathématique de France, 1988.

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Tschinkel, Yuri, Carlo Gasbarri, Steven Lu, and Mike Roth. Rational points, rational curves, and entire holomorphic curves on projective varieties: CRM short thematic program, June 3-28, 2013, Centre de Recherches Mathematiques, Universite de Montreal, Quebec, Canada. American Mathematical Society, 2015.

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3

Shlomo, Ta'asan, and Institute for Computer Applications in Science and Engineering., eds. The algebraic multigrid projection for eigenvalue problems; backrotations and multigrid fixed points. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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4

Huybrechts, D. Fourier-Mukai Transforms in Algebraic Geometry. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.001.0001.

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This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of
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Hrushovski, Ehud, and François Loeser. Introduction. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0001.

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This book deals with non-archimedean tame topology and stably dominated types. It considers o-minimality as an analogy and reduces questions over valued fields to the o-minimal setting. A fundamental tool, imported from stability theory, is the notion of a definable type, which plays a number of roles, starting from the definition of a point of the fundamental spaces. One of the roles of definable types is to be a substitute for the classical notion of a sequence, especially in situations where one is willing to refine to a subsequence. To each algebraic variety V over a valued field K, the bo
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Book chapters on the topic "Algebraic point projection"

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Poonen, Bjorn. "The Hasse Principle for Complete Intersections in Projective Space." In Rational Points on Algebraic Varieties. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8368-9_11.

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Klyachko, Alexander A. "Spatial Polygons and Stable Configurations of Points in the Projective Line." In Algebraic Geometry and its Applications. Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-322-99342-7_8.

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"Configurations of six points." In Pencils of Cubics and Algebraic Curves in the Real Projective Plane. Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9780429451959-14.

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"Configurations of seven points." In Pencils of Cubics and Algebraic Curves in the Real Projective Plane. Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9780429451959-15.

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"Points, lines and conics in the plane." In Pencils of Cubics and Algebraic Curves in the Real Projective Plane. Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9780429451959-13.

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Green, Mark, Phillip Griffiths, and Matt Kerr. "The Mumford-Tate Group of a Variation of Hodge Structure." In Mumford-Tate Groups and Domains. Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691154244.003.0004.

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This chapter deals with the Mumford-Tate group of a variation of Hodge structure (VHS). It begins by presenting a definition of VHS, which consists of a connected complex manifold and a locally liftable, holomorphic mapping that is an integral manifold of the canonical differential ideal. The moduli space of Γ‎-equivalence classes of polarized Hodge structures is also considered, along with a generic point for the VHS and the monodromy group of the VHS. Associated to a VHS is its Mumford-Tate group. The chapter proceeds by discussing the structure theorem for VHS, where S is a quasi-projective algebraic variety, referred to as global variations of Hodge structure. It concludes by describing an application of Mumford-Tate groups, along with the Noether-Lefschetz locus.
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Lam, Ngau. "On the conjecture of the resolution of a finite set of points in projective space." In First International Tainan-Moscow Algebra Workshop, edited by Y. Fong, U. Knauer, and A. V. Mikhalev. De Gruyter, 1996. http://dx.doi.org/10.1515/9783110883220-015.

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Conference papers on the topic "Algebraic point projection"

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Chen, XiaoDiao, Yin Zho, Zhenyu Shu, and Hua Su. "Improved Algebraic Algorithm on Point projection for B´eziercurves." In Second International Multi-Symposiums on Computer and Computational Sciences (IMSCCS 2007). IEEE, 2007. http://dx.doi.org/10.1109/imsccs.2007.17.

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Chen, XiaoDiao, Yin Zhou, Zhenyu Shu, and Hua Su. "Improved Algebraic Algorithm on Point projection for B´eziercurves." In Second International Multi-Symposiums on Computer and Computational Sciences (IMSCCS 2007). IEEE, 2007. http://dx.doi.org/10.1109/imsccs.2007.4392595.

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MORI, IZURU. "NONCOMMUTATIVE PROJECTIVE SCHEMES AND POINT SCHEMES." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0014.

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Purwar, Anurag, and Q. J. Ge. "Polar Decomposition of Unit Dual Quaternions." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70882.

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This paper seeks to extend the notion of polar decomposition from matrix algebra to dual quaternion algebra. The goal is to obtain a simple, efficient and explicit method for determining the polar decompositions (PD) of spatial displacements in Euclidean three-space that belong to a special Euclidean Group known as SE(3). It has been known that such a decomposition is equivalent to the projection of an element of SE(3) onto SO(4) that yields hyper spherical displacements that best approximate rigid-body displacements. It is shown in this paper that a dual quaternion representing an element of
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Bayro-Corrochano, E., J. Lasenby, and G. Sommer. "Geometric algebra: a framework for computing point and line correspondences and projective structure using n uncalibrated cameras." In Proceedings of 13th International Conference on Pattern Recognition. IEEE, 1996. http://dx.doi.org/10.1109/icpr.1996.546044.

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Wu, Jun, Anurag Purwar, and Q. J. Ge. "Interactive Dimensional Synthesis and Motion Design of Planar 6R Closed Chains via Constraint Manifold Modification." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87818.

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In this paper, we present an interactive, visual design approach for the dimensional synthesis of planar 4R, 5R, and 6R closed chains for a given rational motion using constraint manifold modification. This approach is implemented in an interactive software tool that provides mechanism designers with an intuitive way to determine the dimensional parameters of planar mechanisms, and in the process equips them with an understanding of the design process. The theoretical foundation of this work is based on representing planar displacements with planar quaternions which can be seen as points in a
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Ravani, B., and Q. J. Ge. "Computation of Spatial Displacements From Geometric Features." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0065.

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Abstract This paper develops the theoretical foundation for computations of spatial displacements from the simple geometric features of points, lines, planes and their combinations. Using an oriented projective three space with a Clifford Algebra, all these three features are handled in a similar fashion. Furthermore, issues related to uniqueness of computations and minimal number of required features are discussed. It is shown that contrary to the common intuition, specification of a minimum of four points (planes) or three lines (each pair being non-planar) are necessary for computation of a
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Hampton, R. David, Nathan S. Wiedenman, and Ting H. Li. "Analytical Determination of Shock Response Spectra for an Impulse-Loaded Proportionally Damped System." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58024.

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Many military systems must be capable of sustained operation in the face of mechanical shocks due to projectile or other impacts. The most widely used method of quantifying a system’s vibratory transient response to shock loading is called the shock response spectrum (SRS). The system response for which the SRS is to be determined can be due, physically, either to a collocated or to a noncollocated shock loading. Taking into account both possibilities, one can define the SRS as follows: the SRS presents graphically the maximum transient response (output) of an imaginary ideal mass-spring-dampe
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Lipkin, Harvey. "On Trigonometric Formulations of Polynomial Equations." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99695.

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The displacement analysis of open and closed kinematic chains is based on polynomial equations whose variables are functions of relative joint displacements. The objective of this paper is to investigate new and interesting properties of the transformations between the canonical cosine-sine polynomials and the even degree tan-half angle polynomials associated with displacement kinematics. Using a homogeneous coordinate formulation, it is shown that the coefficients of the polynomials are linearly related by a projective transformation whose elements can be defined recursively. The canonical co
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