Relevant bibliographies by topics / Plane trigonometry Trigonometry

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  1. Journal articles
  2. Dissertations / Theses
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Academic literature on the topic 'Plane trigonometry Trigonometry'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 February 2022

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Journal articles on the topic "Plane trigonometry Trigonometry"

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Moussa, Ali. "MATHEMATICAL METHODS IN ABŪ AL-WAFĀʾ'S ALMAGEST AND THE QIBLA DETERMINATIONS". Arabic Sciences and Philosophy 21, № 1 (2011): 1–56. http://dx.doi.org/10.1017/s095742391000007x.

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AbstractThe problem of the Qibla was one of the central issues in the scientific culture of Medieval Islam, and to solve it properly, one needed mathematics and observation. The mathematics consisted of two parts: plane trigonometry (to construct the trigonometric tables) and spherical trigonometry (as the problem belongs to spherical astronomy). Observation and its instruments were needed to find the geographical coordinates of Mecca and the given location; these coordinates (latitude, longitude) will be the input data in the formulas of the Qibla. In his Almagest, Abū al-Wafāʾ produced a brilliant work to solve the problem. He worked on both mathematics and observation, and reached accurate and easy “modern” solutions. In plane trigonometry, he introduced the trigonometric functions with new definitions, proved the formulas for sines, approximated the sine of degree one, and thus constructed the tables of sines and tangents with high accuracy. In spherical trigonometry, he proved four new spherical theorems, including the tangent rule (which was based on the new definitions and this rule allowed him to work out the easiest solution, as will be shown). In observation, he described three instruments which he used over several years in Baghdad. This paper is a detailed technical and analytical description of Abū al-Wafāʾ's mathematical methods and the Qibla determinations, supplemented with many important original Arabic texts with translation and commentary.
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Conway, John, and Alex Ryba. "Remembering spherical trigonometry." Mathematical Gazette 100, no. 547 (2016): 1–8. http://dx.doi.org/10.1017/mag.2016.3.

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Although high school textbooks from early in the 20th century show that spherical trigonometry was still widely taught then, today very few mathematicians have any familiarity with the subject. The first thing to understand is that all six parts of a spherical triangle are really angles — see Figure 1.This shows a spherical triangle ABC on a sphere centred at O. The typical side is a = BC is a great circle arc from to that lies in the plane OBC; its length is the angle subtended at O. Similarly, the typical angle between the two sides AB and AC is the angle between the planes OAB and OAC.
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Insel, Arnold J. "Rotation Matrices in the Plane without Trigonometry." College Mathematics Journal 24, no. 1 (1993): 71. http://dx.doi.org/10.2307/2686436.

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Insel, Arnold J. "Rotation Matrices in the Plane without Trigonometry." College Mathematics Journal 24, no. 1 (1993): 71–73. http://dx.doi.org/10.1080/07468342.1993.11973510.

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Insel, Arnold J. "Rotation Matrices in the Plane without Trigonometry." College Mathematics Journal 24, no. 1 (1993): 71–73. http://dx.doi.org/10.1080/07468342.1993.12345744.

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Ingarden, R. S., and L. Tamássy. "On Parabolic Trigonometry in a Degenerate Minkowski Plane." Mathematische Nachrichten 145, no. 1 (1990): 87–95. http://dx.doi.org/10.1002/mana.19901450107.

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Coxeter, H. S. M. "The Trigonometry of Hyperbolic Tessellations." Canadian Mathematical Bulletin 40, no. 2 (1997): 158–68. http://dx.doi.org/10.4153/cmb-1997-019-0.

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AbstractFor positive integerspandqwith (p− 2)(q− 2) > 4 there is, in the hyperbolic plane, a group [p, q] generated by reflections in the three sides of a triangleABCwith angles π/p, π/q, π/2. Hyperbolic trigonometry shows that the sideAChas length ψ, where cosh ψ =c/s, c = cos π/q,s= sin π/p. For a conformal drawing inside the unit circle with centreA, we may take the sidesABandACto run straight along radiiwhileBCappears as an arc of a circle orthogonal to the unit circle. The circle containing this arc is found to have radius 1/ sinh ψ =s/z, where z =, while its centre is at distance 1/ tanh ψ = c/z fromA. In the hyperbolic triangleABC, the altitude fromABto the right-angled vertex C is ζ, where sinh ζ = z.
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Phan-Yamada, Tuyetdong, and Walter M. Yamada. "Exploroing Polar Curves with GeoGebra." Mathematics Teacher 106, no. 3 (2012): 228–33. http://dx.doi.org/10.5951/mathteacher.106.3.0228.

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Most trigonometry textbooks teach the graphing of polar equations as a two-step process: (1) plot the points corresponding to values of θ such as π, π/2, π/3, π/4, π/6, and so on; and then (2) connect these points with a curve that follows the behavior of the trigonometric function in the Cartesian plane. Many students have difficulty using this method to graph general polar curves. The difficulty seems to stem from an inability to convert changes in the value of the trigonometric equation as a function of angle (abscissa vs. ordinate in Cartesian coordinates) to changes of the radius as a function of angle (r[θ] in polar coordinates). GeoGebra provides a tool to help students visualize this relationship, thus significantly improving students' ability
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Mathar, R. J. "Spherical trigonometry of the projected baseline angle." Serbian Astronomical Journal, no. 177 (2008): 115–24. http://dx.doi.org/10.2298/saj0877115m.

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The basic vector geometry of a stellar interferometer with two telescopes is defined by the right triangle of (i) the baseline vector between the telescopes, of (ii) the delay vector which points to the star, and of (iii) the projected baseline vector in the plane of the wave front of the stellar light. The plane of this triangle intersects the celestial sphere at the position of the star; the intersection is a circular line segment. The interferometric angular resolution is high (diffraction limited to the ratio of the wavelength over the projected baseline length) in the two directions along this line segment, and low (diffraction limited to the ratio of the wavelength over the telescope diameter) perpendicular to these. The position angle of these characteristic directions in the sky is calculated here, given either local horizontal coordinates, or celestial equatorial coordinates.
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Chatelin, Françoise, and M. Monserrat Rincon-Camacho. "Hermitian matrices: Spectral coupling, plane geometry/trigonometry and optimisation." Linear Algebra and its Applications 533 (November 2017): 282–310. http://dx.doi.org/10.1016/j.laa.2017.07.009.

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Dissertations / Theses on the topic "Plane trigonometry Trigonometry"

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Brown, Susan A. Presmeg Norma C. "The trigonometric connection students' understanding of sine and cosine /." Normal, Ill. : Illinois State University, 2005. http://proquest.umi.com/pqdweb?index=0&did=1251811011&SrchMode=1&sid=2&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1176384631&clientId=43838.

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Thesis (Ph. D.)--Illinois State University, 2005.<br>Title from title page screen, viewed April 12, 2007. Dissertation Committee: Norma C. Presmeg (chair), John A. Dossey, Michael J. Plantholt. Includes bibliographical references (leaves 253-261) and abstract. Also available in print.
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Cook, Gary Russell. "Arcs in a finite projective plane." Thesis, University of Sussex, 2011. http://sro.sussex.ac.uk/id/eprint/7510/.

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The projective plane of order 11 is the dominant focus of this work. The motivation for working in the projective plane of order 11 is twofold. First, it is the smallest projective plane of prime power order such that the size of the largest (n, r)-arc is not known for all r ∈ {2,...,q + 1}. It is also the smallest projective plane of prime order such that the (n; 3)-arcs are not classified. Second, the number of (n, 3)-arcs is significantly higher in the projective plane of order 11 than it is in the projective plane of order 7, giving a large number of (n, 3)-arcs for study. The main application of (n, r)-arcs is to the study of linear codes. As a forerunner to the work in the projective plane of order eleven two algorithms are used to raise the lower bound on the size of the smallest complete n-arc in the projective plane of order thirty-one from 12 to 13. This work presents the classification up to projective equivalence of the complete (n, 3)- arcs in PG(2, 11) and the backtracking algorithm that is used in its construction. This algorithm is based on the algorithm used in [3]; it is adapted to work on (n, 3)-arcs as opposed to n-arcs. This algorithm yields one representative from every projectively inequivalent class of (n, 3)-arc. The equivalence classes of complete (n, 3)-arcs are then further classified according to their stabilizer group. The classification of all (n, 3)-arcs up to projective equivalence in PG(2, 11) is the foundation of an exhaustive search that takes one element from every equivalence class and determines if it can be extended to an (n′, 4)-arc. This search confirmed that in PG(2, 11) no (n, 3)-arc can be extended to a (33, 4)-arc and that subsequently m4(2, 11) = 32. This same algorithm is used to determine four projectively inequivalent complete (32, 4)-arcs, extended from complete (n, 3)-arcs. Various notions under the general title of symmetry are defined both for an (n, r)-arc and for sets of points and lines. The first of these makes the classification of incomplete (n; 3)- arcs in PG(2, 11) practical. The second establishes a symmetry based around the incidence structure of each of the four projectively inequivalent complete (32, 4)-arcs in PG(2, 11); this allows the discovery of their duals. Both notions of symmetry are used to analyze the incidence structure of n-arcs in PG(2, q), for q = 11, 13, 17, 19. The penultimate chapter demonstrates that it is possible to construct an (n, r)-arc with a stabilizer group that contains a subgroup of order p, where p is a prime, without reference to an (m < n, r)-arc, with stabilizer group isomorphic to ℤ1. This method is used to find q-arcs and (q + 1)-arcs in PG(2, q), for q = 23 and 29, supporting Conjecture 6.7. The work ends with an investigation into the effect of projectivities that are induced by a matrix of prime order p on the projective planes. This investigation looks at the points and subsets of points of order p that are closed under the right action of such matrices and their structure in the projective plane. An application of these structures is a restriction on the size of an (n, r)-arc in PG(2, q) that can be stabilized by a matrix of prime order p.
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Al-Zangana, Emad Bakr Abdulkareem. "The geometry of the plane of order nineteen and its application to error-correcting codes." Thesis, University of Sussex, 2011. http://sro.sussex.ac.uk/id/eprint/7427/.

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In the projective space PG(k−1; q) over Fq, the finite field of order q, an (n; r)-arc K is a set of n points with at most r on a hyperplane and there is some hyperplane meeting K in exactly r points. An arc is complete if it is maximal with respect to inclusion. The arc K corresponds to a projective [n; k;n − r]q-code of length n, dimension k, and minimum distance n − r; if K is a complete arc, then the corresponding projective code cannot be extended. In this thesis, the n-sets in PG(1; 19) up to n = 10 and the n-arcs in PG(2; 19) for 4 B n B 20 in both the complete and incomplete cases are classified. The set of rational points of a non-singular, plane cubic curve can be considered as an arc of degree three. Over F19, these curves are classified, and the maximum size of the complete arc of degree three that can be constructed from each such incomplete arc is given.
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Soares, Vanessa Ribeiro. "Batalha naval e suas aplicações." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/5909.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-08-10T13:40:03Z No. of bitstreams: 2 Dissertação - Vanessa Ribeiro Soares - 2016.pdf: 11844437 bytes, checksum: 03d509603ea96f2647ea2764aea87d17 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-10T13:42:09Z (GMT) No. of bitstreams: 2 Dissertação - Vanessa Ribeiro Soares - 2016.pdf: 11844437 bytes, checksum: 03d509603ea96f2647ea2764aea87d17 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made available in DSpace on 2016-08-10T13:42:09Z (GMT). No. of bitstreams: 2 Dissertação - Vanessa Ribeiro Soares - 2016.pdf: 11844437 bytes, checksum: 03d509603ea96f2647ea2764aea87d17 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-05-30<br>This work has the purpose contribute to the improvement in some teaching contents of analytic geometry and trigonometry in high school . The content work was based on the National Curriculum Parameters, highlighting de nitions, theorems and properties necessary for the development of student learning. The theme was chosen after a practical experience involving the Naval Battle game in order to reduce the students' di culties. The playful work, as the game, has a practical application that does the student become familiar with the content. That's an interesting way to propose problems and solutions involving the content. Thus becomes something attractive to the student and encourages creativity in nding problems solutions.<br>O trabalho tem como objetivo contribuir para o aprimoramento no ensino de alguns conteúdos de Geometria Analítica e Trigonometria no Ensino Médio. Dentro dos Parâmetros Curriculares Nacionais, trabalhamos o conteúdo destacando de nições, teoremas e propriedades necessárias para o desenvolvimento de aprendizagem do aluno. O tema foi escolhido depois de uma experiência prática envolvendo o jogo Batalha Naval a m de diminuir as di culdades dos alunos. O trabalho lúdico, como o jogo, tem uma aplicação prática que faz o aluno se familiarizar com os conceitos. É uma forma interessante de propor problemas e soluções envolvendo o conceitos. Assim se torna algo atrativo para o aluno e favorece a criatividade na busca de soluções para os problemas.
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Mendes, Cleiton Dias. "Demonstrações trigonométricas via geometria plana." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/3981.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-27T14:44:19Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cleiton Dias Mendes - 2014.pdf: 3423618 bytes, checksum: af330c6c7d1a32cfc2168c6edd4a9f79 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-28T12:57:43Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cleiton Dias Mendes - 2014.pdf: 3423618 bytes, checksum: af330c6c7d1a32cfc2168c6edd4a9f79 (MD5)<br>Made available in DSpace on 2015-01-28T12:57:43Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cleiton Dias Mendes - 2014.pdf: 3423618 bytes, checksum: af330c6c7d1a32cfc2168c6edd4a9f79 (MD5) Previous issue date: 2014-08-06<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>This work has been presented with some trigonometric connections statements only using plane geometry. This proceeding has been realized because we observed that a didactic book only presents algebraic statements. We wish in this way, presents to mathematics teachers and students in high or upper school, trigonometry statements identity using geometry. For this, It has been considered trigonometry cycle only in the first quadrant, given an angle such that α have any α ˂ 90°, extending the reasoning to the other quadrants.<br>O presente trabalho tem como objetivo apresentar as demonstrações de algumas relações trigonométricas utilizando somente a geometria plana. Este procedimento foi realizado visto que a maioria dos livros didáticos apresentam demonstrações quase que somente algébricas. Desejamos desta forma, apresentar aos professores e aos alunos de matemática do ensino médio e/ou superior, as demonstrações de identidades trigonométricas utilizando a geometria. Para isso foi considerado o ciclo trigonométrico apenas no primeiro quadrante, tal que dado um ângulo α qualquer temos α ˂ 90°, estendendo o raciocínio aos demais quadrantes.
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Laird, Daniel T. "Geometric Model for Tracker-Target Look Angles and Line of Sight Distance." International Foundation for Telemetering, 2015. http://hdl.handle.net/10150/596399.

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ITC/USA 2015 Conference Proceedings / The Fifty-First Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2015 / Bally's Hotel & Convention Center, Las Vegas, NV<br>To determine the tracking abilities of a Telemetry (TM) antenna control unit (ACU) requires 'truth data' to analyze the accuracy of measured, or observed tracking angles. This requires we know the actual angle, i.e., that we know where the target is above the earth. The positional truth is generated from target time-space position information (TSPI), which implicitly places the target's global positioning system (GPS) as the source of observational accuracy. In this paper we present a model to generate local look-angles (LA) and line-of-sight (LoS) distance with respect to (w.r.t.) target global GPS. We ignore inertial navigation system (INS) data in generating relative position at time T; thus we model the target as a global point in time relative to the local tracker's global fixed position in time. This is the first of three companion papers on tracking This is the first of three companion papers on tracking analyses employing Statistically Defensible Test & Evaluation (SDT&E) methods.
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Pichanick, E. V. D. "Bounds for complete arcs in finite projective planes." Thesis, University of Sussex, 2016. http://sro.sussex.ac.uk/id/eprint/63459/.

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This thesis uses algebraic and combinatorial methods to study subsets of the Desarguesian plane IIq = PG(2, q). Emphasis, in particular, is given to complete (k, n)-arcs and plane projective curves. Known Diophantine equations for subsets of PG(2, q), no more than n of which are collinear, have been applied to k-arcs of arbitrary degree. This yields a new lower bound for complete (k, n)-arcs in PG(2, q) and is a generalization of a classical result of Barlotti. The bound is one of few known results for complete arcs of arbitrary degree and establishes new restrictions upon the parameters of associated projective codes. New results governing the relationship between (k, 3)-arcs and blocking sets are also provided. Here, a sufficient condition ensuring that a blocking set is induced by a complete (k, 3)-arc in the dual plane q is established and shown to complement existing knowledge of relationships between k-arcs and blocking sets. Combinatorial techniques analyzing (k, 3)-arcs in suitable planes are then introduced. Utilizing the numeric properties of non-singular cubic curves, plane (k, 3)-arcs satisfying prescribed incidence conditions are shown not to attain existing upper bounds. The relative sizes of (k, 3)-arcs and non-singular cubic curves are also considered. It is conjectured that m3(2, q), the size of the largest complete (k, 3)-arc in PG(2, q), exceeds the number of rational points on an elliptic curve. Here, a sufficient condition for its positive resolution is given using combinatorial analysis. Exploiting its structure as a (k, 3)-arc, the elliptic curve is then considered as a method of constructing cubic arcs and results governing completeness are established. Finally, classical theorems relating the order of the plane q to the existence of an elliptic curve with a specified number of rational points are used to extend theoretical results providing upper bounds to t3(2, q), the size of the smallest possible complete (k, 3)-arc in PG(2, q).
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Loreto, Junior Armando Pereira. "Uma obra do matemático jesuíta Manuel de Campos para a "Aula da esfera" do Colégio Santo Antão." Pontifícia Universidade Católica de São Paulo, 2001. https://tede2.pucsp.br/handle/handle/13250.

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Made available in DSpace on 2016-04-28T14:16:13Z (GMT). No. of bitstreams: 1 Armando Pereira Loreto Junior.pdf: 1989486 bytes, checksum: b270828c0f687f19dacbba6800156d40 (MD5) Previous issue date: 2001-06-26<br>This research investigates which were the mathematical contents, sequence and manner of exposition taught in the sphere class of Colégio de Santo Antão-OVelho, in Lisbon, during the second half of the 18th century. The current work describes, within the context of that time, the most relevant features of the compendium Trigonometria Plana e Esferica com o Canon Trigonometrico, Linear e Logarithmico, published in 1737. Its author is the Jesuit priest Manoel de Campos, who was one of the teachers of that class. This study reveals interesting approaches made by him, which led to important results, like the correction of the Canon Trigonometrico, and the generation of the logarithmic curve. It was verified that the trigonometry presented by Campos had as its first objective the application to the Nautical Science and Astronomy. However, the author did not present these applications in his book, but promised to show them in another publication, which existence we did not find register of. Because of that, some examples of those applications, included in Arte de Navegar of Manoel Pimentel, were selected and presented in this work<br>Esta pesquisa investiga quais eram os conteúdos de matemática ensinados, sua ordem seqüencial e a forma de exposição, na aula da esfera do Colégio de Santo Antão-O-Velho da cidade de Lisboa, na primeira metade do século XVIII. O presente trabalho descreve, dentro do contexto científico daquela época, os aspectos mais relevantes do compêndio Trigonometria Plana e Esferica com o Canon Trigonometrico, Linear e Logarithmico, publicado em 1737, cujo autor é o padre jesuíta Manoel de Campos, que foi um dos professores daquela aula. Este estudo revela abordagens interessantes por ele efetuadas, que conduziram a resultados importantes, como a correção do Canon Trigonometrico e a geração da linha logarítmica. Ficou constatado que a trigonometria apresentada por Campos tinha como primeiro objetivo a sua aplicação à náutica e à astronomia. Contudo, o autor não apresentou tais aplicações no seu compêndio, prometendo mostrá-las oportunamente em outra publicação, de cuja existência não encontramos registro. Em virtude disso, alguns exemplos dessas aplicações, contidos na Arte de Navegar de Manoel Pimentel, contemporâneo de Campos, foram selecionados e apresentados neste trabalho
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Bezerra, Antônio Almir. "Relações trigonométricas fundamentais." reponame:Repositório Institucional da UFC, 2014. http://www.repositorio.ufc.br/handle/riufc/8744.

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BEZERRA, Antônio Almir. Relações trigonométricas fundamentais. 2014. 59 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014.<br>Submitted by Erivan Almeida (eneiro@bol.com.br) on 2014-08-18T18:26:02Z No. of bitstreams: 1 Dissertacao de Antonio Almir Bezerra.pdf: 1732043 bytes, checksum: 6d0f5917cd52b68f851df7a78b900192 (MD5)<br>Approved for entry into archive by Rocilda Sales(rocilda@ufc.br) on 2014-08-19T15:35:37Z (GMT) No. of bitstreams: 1 Dissertacao de Antonio Almir Bezerra.pdf: 1732043 bytes, checksum: 6d0f5917cd52b68f851df7a78b900192 (MD5)<br>Made available in DSpace on 2014-08-19T15:35:37Z (GMT). No. of bitstreams: 1 Dissertacao de Antonio Almir Bezerra.pdf: 1732043 bytes, checksum: 6d0f5917cd52b68f851df7a78b900192 (MD5) Previous issue date: 2014<br>The present research aims to present classic demonstrations of the fundamental relations of Trigonometry,with a simple approach, and exploring flat shapes. The intention is to make such demonstrations better known and provide a highlight for Trigonometry, since they are essential in solving problems of everyday life. For this purpose, we made a historical highlighting of the importance of trigonometry in the mathematical context. Since we know Trigonometry is loosing its status and not being considered essential in basic education anymore, such demonstrations, associated with the flat shapes, may be used as a model class. Therefore, we highlight the following fundamental relations: Basic Trigonometric relations, Derived Relations, Sine of the Sum and Difference of Two Arcs, Cosine of the Sum and Difference of Two Arcs, Double Arcs, Half Arc, Transformation in Product and Applications. For the demonstration ot these relations we used some area results, cosine law, Ptolemy’s theorem and the theorem of the broken chord Plane Geometry. We believe that Trigonometry is linked to the formation of these flat shapes. Thus, such demonstrationas associated to these flat shapes may serve to improve the Trigonometry teaching- learning and as motivator for students and teachers seeking to enhance their knowledge in mathematics.<br>Neste trabalho apresentamos algumas relações trigonométricas fundamentais e suas demonstrações. Tais relações merecem destaque, pois são essenciais na resolução de problemas nas diversas áreas do conhecimento. Inicialmente fizemos um breve histórico da Trigonometria destacando a sua importância no contexto da Matemática. Em sequência apresentamos as relações fundamentais, dentre elas, enfatizamos as fórmulas da adição de arcos, cujas demonstrações utilizamos área de figuras planas, a lei dos cossenos e a lei dos senos. Além disso, mostramos como estas fórmulas se relacionam com o Teorema da Corda Quebrada e o Teorema de Ptolomeu da Geometria Plana. Explorando a relações entre Trigonometria e Geometria Plana. Procuramos mostrar a importância desta teoria no ensino médio motivando alunos e professores a buscar um maior interesse pelo conhecimento em Matemática.
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Santos, José Adriano Fernandes dos. "Matemática aplicada à geografia." reponame:Repositório Institucional da UFC, 2016. http://www.repositorio.ufc.br/handle/riufc/17457.

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SANTOS, José Adriano Fernandes dos. Matemática aplicada à geografia. 2016. 50 f. Dissertação (Mestrado em Matemática em Rede Nacional) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016.<br>Submitted by Rocilda Sales (rocilda@ufc.br) on 2016-06-06T12:40:38Z No. of bitstreams: 1 2016_dis_jafsantos.pdf: 902713 bytes, checksum: 4ea384ffd89385f06029fe054cb14ba1 (MD5)<br>Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-06-06T12:41:14Z (GMT) No. of bitstreams: 1 2016_dis_jafsantos.pdf: 902713 bytes, checksum: 4ea384ffd89385f06029fe054cb14ba1 (MD5)<br>Made available in DSpace on 2016-06-06T12:41:14Z (GMT). No. of bitstreams: 1 2016_dis_jafsantos.pdf: 902713 bytes, checksum: 4ea384ffd89385f06029fe054cb14ba1 (MD5) Previous issue date: 2016<br>From the interdisciplinary scenario in which mathematics is, this work comes down to present applications coming from Geography within the mathematical context. The NCP's (1998), documents governing the current Brazilian education, makes clear the importance of interdisciplinary work in education, and the importance of a contextualized teaching based on practical and historical experience of man. In turn, the geography was seen that mapping brings outstanding contributions to mathematics, and trigonometry is one of the main tools used in this context, both by the Euclidean geometry as the non-Euclidean geometry. So in this paper were presented some applications withdrawn from the study of cartography, with the help of mathematics and especially Trigonometry (flat and spherical) were resolved. Continuing, still focusing on cartography, specifically in the study of maps and projections, emphasis was given to Cylindrical Mercator projection and their mathematical explanations for the so-called art of designing a plan in case the projection of the sphere in a plane, with its appropriate mathematical explanations for such a feat. With time and the emergence of infinitesimal calculus, it was shown here to determine the variable called Mercator and its origin. Then with the help of differential geometry emphasizing Gauss studies, it was presented not isometry between the plane and the sphere, and the Gaussian curvature is the defining function for this fact. Through the fundamental forms and egregious Theorem here also presented the Gauss studies in differential geometry were defining for the most current explanation of Mercator variable, thus contributing to the clarification of the famous projection made by Mercator that went down in history for its perfection.<br>Partindo do cenário interdisciplinar em que a Matemática se encontra, este trabalho se resume a apresentar aplicações oriundos da Geografia dentro da contextualização matemática. Os PCN’s (1998), documentos que regem a educação atual brasileira, deixa clara importância do trabalho interdisciplinar no ensino, bem como a relevância de um ensinamento contextualizado baseado na pratica e vivência histórica do homem. Por sua vez, na Geografia foi visto que a cartografia traz contribuições relevantes à matemática, e que a trigonometria é uma das ferramentas principais utilizadas nesta conjuntura, tanto por parte da geometria euclidiana quanto da geometria não-euclidiana. Assim neste trabalho foram apresentadas algumas aplicações retiradas do estudo da cartografia que, com a ajuda da matemática e principalmente da trigonometria (plana e esférica) foram resolvidas. Dando sequência, ainda com foco na cartografia, especificamente no estudo de mapas e projeções, foi dada ênfase à Projeção Cilíndrica de Mercator e respectivas explicações matemáticas para a chamada arte de projetar num plano, no caso, à projeção da esfera num plano, com suas devidas explicações matemáticas para tal feito. Com o tempo e o surgimento do cálculo infinitesimal, foi mostrado aqui a determinação da chamada variável de Mercator, e sua origem. Em seguida com a ajuda da Geometria Diferencial dando ênfase aos estudos de Gauss, foi apresentada a não isometria entre o plano e a esfera, e que a curvatura gaussiana é a função definidora para tal fato. Através das formas fundamentais e do Teorema egrégio aqui também apresentadas, os estudos de Gauss dentro da geometria diferencial foram definidores para a explicação mais atual da variável de Mercator, contribuindo assim para o esclarecimento da famosa projeção feita por Mercator que ficou na história por sua perfeição.
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Books on the topic "Plane trigonometry Trigonometry"

1

Rice, Bernard J. Plane trigonometry. 6th ed. PWS-Kent Pub. Co., 1992.

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Gustafson, R. David. Plane trigonometry. 3rd ed. Brooks/Cole Pub. Co., 1989.

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Gustafson, R. David. Plane trigonometry. 4th ed. Brooks/Cole Pub. Co., 1994.

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Rice, Bernard J. Plane trigonometry. 7th ed. PWS Pub. Co., 1996.

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Dalton, Tarwater J., ed. Plane trigonometry. 7th ed. McGraw-Hill, 1993.

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Heineman, E. Richard. Plane trigonometry. 6th ed. McGraw-Hill, 1988.

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Rice, Bernard J. Plane trigonometry. 4th ed. Prindle, Weber & Schmidt, 1986.

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Rice, Bernard J. Plane trigonometry. 5th ed. PWS-Kent Pub. Co., 1989.

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Steinlage, Ralph C. Trigonometry. West, 1985.

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P, Abbott. Trigonometry. NTC Pub. Group, 1992.

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Book chapters on the topic "Plane trigonometry Trigonometry"

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Haines, Betty, Roger Haines, and Andrew May. "Plane trigonometry." In Mathematics A Level. Macmillan Education UK, 1996. http://dx.doi.org/10.1007/978-1-349-13850-0_7.

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Ghosh, Debdas, and Debjani Chakraborty. "Fuzzy Triangle and Fuzzy Trigonometry." In An Introduction to Analytical Fuzzy Plane Geometry. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15722-7_4.

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Fleurant, Cyril, and Sandrine Bodin-Fleurant. "Trigonometry, Geometry of Plane and Space." In Springer Textbooks in Earth Sciences, Geography and Environment. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-69242-5_3.

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Harris, John W., and Horst Stocker. "Geometry and trigonometry in the plane." In Handbook of Mathematics and Computational Science. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-5317-4_3.

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Catoni, Francesco, Dino Boccaletti, Roberto Cannata, Vincenzo Catoni, and Paolo Zampetti. "Trigonometry in the Hyperbolic (Minkowski) Plane." In Geometry of Minkowski Space-Time. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17977-8_4.

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Peng, De-jun, and Shen Youjian. "Trigonometric Wavelet Methods for the Plane Elasticity Problem." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-02777-3_24.

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Rassias, Michael Th, Bicheng Yang, and Andrei Raigorodskii. "On a Half-Discrete Hilbert-Type Inequality in the Whole Plane with the Kernel of Hyperbolic Secant Function Related to the Hurwitz Zeta Function." In Trigonometric Sums and Their Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37904-9_11.

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"Plane and Spherical Trigonometry." In Mathematical Techniques in GIS. CRC Press, 2014. http://dx.doi.org/10.1201/b16910-13.

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"Plane and Spherical Trigonometry." In Mathematical Techniques in GIS, Second Edition. CRC Press, 2014. http://dx.doi.org/10.1201/b16910-6.

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"Plane and Spherical Trigonometry." In Introduction to Mathematical Techniques used in GIS. CRC Press, 2004. http://dx.doi.org/10.1201/b12829-5.

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Conference papers on the topic "Plane trigonometry Trigonometry"

1

Sadr, Mohammad Homayoun, Hadi Ghashochi Bargh, Mostafa Khorram Nejadi, and Hoofar Pourzand. "Free Vibration Analysis of Rotating Laminated Composite Panels Using Finite Strip Method With Modified Shape Functions." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62269.

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In this paper, free vibration analysis of rotating laminated composite panels is investigated. The formulation is based on the classical laminated plate theory (CLPT), and the method of analysis is the semi-analytical finite strip approach which has been developed on the basis of full energy method with modified shape functions. In the longitudinal direction, the combinations of trigonometric and polynomial functions are used for the out-of-plane displacements, and the trigonometric functions are utilized to estimate the in-plane displacements, to satisfy the kinematic conditions prescribed at the two ends of the strip. Also in the transverse direction, the Hermite cubic shape functions are used for the out-of-plane displacements and the first-order Lagrange shape functions are applied for the in-plane displacements. The panel is considered to be clamped at the rim of a central hub and is free along the other three edges. The effects of different parameters including length/width ratio, number of layers, fiber orientation angles, rotation speed on dimensionless natural frequencies are investigated and discussed in the paper. To check the validity, the results generated by the finite strip procedure are compared with the results of previous studies and finite element code, wherever possible.
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Gupta, Ankit, and Mohammad Talha. "A New Trigonometric Higher-Order Shear and Normal Deformation Theory for Functionally Graded Plates." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66771.

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In the present study, a new trigonometric higher-order shear and normal deformation theory is proposed and implemented to investigate the free vibration characteristics of functionally graded material (FGM) plates. The present theory comprises the nonlinear variation in the in-plane and transverse displacement and accommodates, both shear deformation and thickness stretching effects. It also satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without requiring any shear correction factor. The governing equations are derived using the variational principle. The effective mechanical properties of FGM plates are assumed to vary according to a power law distribution of the volume fraction of the constituents. Poisson’s ratios of FGM plates are assumed constant. The numerical solution has been obtained using an efficient displacement based C0 finite element model with eight degrees of freedom per node. The computed results are compared with 3-dimensional and quasi-3-dimensional solutions and those projected by other well-known plate theories. Natural frequencies of the functionally graded plates with various side-to-thickness ratios, boundary conditions, and volume fraction index ‘n’ have been computed. It can be concluded that the proposed model is not only accurate but also simple in predicting the vibration behavior of functionally graded plates.
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Chauda, Gaurav, and Daniel J. Segalman. "Two-Dimensional Contact Analysis Using Trigonometric Polynomials: Some Early Verification Problems." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-86099.

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A discretization strategy for elastic contact on a half plane has been devised to explore the significance of different friction models on joint-like interface mechanics. It is necessary to verify that discretization and accompanying contact algorithm on known solutions. An extensive comparison of numerical predictions of this model with corresponding 2-D elastic, frictional contact solutions from the literature is presented.
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Pao, Y. C., P. Y. Qin, and Q. S. Yuan. "A Fast Sequential Hidden-Line Removal Algorithm." In ASME 1993 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/cie1993-0079.

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Abstract A fast hidden-line removal algorithm for single convex or concave object, and multiple objects has been developed. It is applicable to both solid objects constructed with planar faces, and with curved surfaces which are represented by meshes. The invisible lines are removed in phases and the computing time in all phases is minimized. Line edges and plane elements involved in the solid object are sorted in the order of their coordinate values. Bounding rectangular boxes are used to determine the overlaps. In place of the trigonometric functions, a simplified linear function is adopted for reducing the computing time. Illustrative examples are presented to demonstrate the practical applications of the developed algorithm.
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Kozˇulovic´, Dragan. "Propulsive Efficiency of Plane and Axisymmetric Nozzles With Non-Uniform Velocity Distributions." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22074.

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The impact of non-uniform velocity distributions at the exit of plane and axisymmetric nozzles is investigated. For this aim, a general equation for the propulsive efficiency has been derived. Velocity profiles of trigonometric and quadratic form, which provide the same thrust force as constant velocity profiles, have been analysed. Only potential effects of the velocity distribution have been investigated. It is shown that the velocity non-uniformities reduce the propulsive efficiency. This reduction is negligible for small non-uniformities, but it can be up to 20% for large non-uniformities. The results indicate that the constant velocity profile is the optimum distribution for the propulsive efficiency.
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Alijani, F., and M. Amabili. "Nonlinear Parametric Instability of Functionally Graded Rectangular Plates in Thermal Environments." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89140.

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Geometrically nonlinear parametric instability of functionally graded (FG) rectangular plates in thermal environments is investigated via multi-modal energy approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to in-plane static and harmonic excitation in the frequency neighbourhood of twice the fundamental frequency is investigated. The boundary conditions are assumed to be simply supported movable. The plate displacements and rotations are expanded in terms of double series trigonometric functions and Lagrange equations are used to reduce the energy functional to a system of infinite nonlinear ordinary differential equations with time varying coefficients, and quadratic and cubic nonlinearities. In order to obtain the complete dynamic scenario, numerical analyses are carried out by means of pseudo arc length continuation and collocation technique to obtain frequency-amplitude and force-amplitude relations in the presence of temperature variation in the thickness direction. The effect of volume fraction exponent as well as temperature variation on the on-set of instability for both static and periodic in-plane excitation are fully discussed and the post-critical nonlinear responses are obtained.
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7

Aluko, O., H. A. Whitworth, and G. Owolabi. "Effect of Friction on Contact Stress Distribution in Pin-Loaded Orthotropic Plates." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-86913.

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An analytical solution is presented for determining the stress distribution in pin loaded composite joints using Lekhnitskii’s complex stress function approach. In this analysis, it is assumed that the pin is rigid, no clearance exists between pin and plate, and Coulomb friction is assumed to act throughout the contact region. The analysis also assumes that the contact boundary at the pin-plate interface spans through half of the hole boundary. The boundary conditions at the pin-plate interface are specified in terms of the trigonometric series used to represent the displacement field in the contact zone. Numerical results are presented for stress distribution in (±45°)s and (04°/±45°)s carbon fibers reinforced laminates.
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Rajalingham, C., R. B. Bhat, and G. D. Xistris. "Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0294.

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Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.
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9

Kinoshita, Shun, Toshiki Hirogaki, Eiichi Aoyama, and Wei Wu. "Skillful Operating of Working Plate to Control Ball Rolling Motion With a Dual Arm Robot." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-64084.

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Industrial dual-arm robots have been gaining attention as novel tools in the field of new automation. Our past research has focused on using them flexibly to control both the linear and rotational motions of a working plate. However, it has been difficult to measure the synchronous accuracy of two rotary axes without a high-accuracy gyro sensor. We therefore developed a novel method to measure the synchronous accuracy of the two rotary axes of a working plate with a ball, in which the ball is kept rolling around a circular path by dual-arm cooperative control. In the present report, in order to widen the range of application, we tried to keep the ball rolling around a rhomboid path, which is one of the polygonal paths used on a working plate by dual-arm cooperative control. It could be seen that there is some possibility of generating an equal speed diamond motion by inputting wave as the odd power of a trigonometric function and considered a deceleration angle with the robot that we handled.
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10

Hashemi, S. M., M. J. Richard, and G. Dhatt. "A Bernoulli-Euler Stiffness Matrix Approach for Vibrational Analysis of Spinning Linearly Tapered Beams." In ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/97-gt-500.

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This paper presents a Dynamic Finite Element (DFE) formulation, based on the Dynamic Stiffness Matrix (DSM) approach, for vibrational analysis of spinning beams. The constituent members are considered to be linearly tapered as well as centrifugally stiffened. A non-dimensional formulation is considered, and the frequency dependent trigonometric shape functions are used to find a single frequency dependent element matrix (called DSM) which has both mass and stiffness properties. An adapted bisection method based on a Sturm sequence root counting technique, is used to find the first four out-of-plane flexural natural frequencies of a cantilevered linearly tapered (in height) beam for different non-dimensional rotating speeds. The results have been compared to those found by finite elements method using Hermite beam elements. Much better convergency rates are found by this method when comparing to conventional finite element methods.
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