The Experts below are selected from a list of 834 Experts worldwide ranked by ideXlab platform
Dinar Camotim - One of the best experts on this subject based on the ideXlab platform.
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on the differentiation of the Rodrigues Formula and its significance for the vector like parameterization of reissner simo beam theory
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Manuel Rittocorrea, Dinar CamotimAbstract:In this paper we present a systematic way of differentiating, up to the second directional derivative, (i) the Rodrigues Formula and (ii) the spin-rotation vector variation relationship. To achieve this goal, several trigonometric functions are grouped into a family of scalar quantities, which can be expressed in terms of a single power series. These results are then applied to the vector-like parameterization of Reissner–Simo beam theory, enabling a straightforward derivation and leading to a clearer Formulation. In particular, and in contrast with previous Formulations, a relatively compact and obviously symmetric form of the tangent operator is obtained. The paper also discusses several relevant issues concerning a beam finite element implementation and concludes with the presentation of a few selected illustrative examples. Copyright © 2002 John Wiley & Sons, Ltd.
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On the differentiation of the Rodrigues Formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Manuel Ritto-corrêa, Dinar CamotimAbstract:In this paper we present a systematic way of differentiating, up to the second directional derivative, (i) the Rodrigues Formula and (ii) the spin-rotation vector variation relationship. To achieve this goal, several trigonometric functions are grouped into a family of scalar quantities, which can be expressed in terms of a single power series. These results are then applied to the vector-like parameterization of Reissner–Simo beam theory, enabling a straightforward derivation and leading to a clearer Formulation. In particular, and in contrast with previous Formulations, a relatively compact and obviously symmetric form of the tangent operator is obtained. The paper also discusses several relevant issues concerning a beam finite element implementation and concludes with the presentation of a few selected illustrative examples. Copyright © 2002 John Wiley & Sons, Ltd.
Manuel Rittocorrea - One of the best experts on this subject based on the ideXlab platform.
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on the differentiation of the Rodrigues Formula and its significance for the vector like parameterization of reissner simo beam theory
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Manuel Rittocorrea, Dinar CamotimAbstract:In this paper we present a systematic way of differentiating, up to the second directional derivative, (i) the Rodrigues Formula and (ii) the spin-rotation vector variation relationship. To achieve this goal, several trigonometric functions are grouped into a family of scalar quantities, which can be expressed in terms of a single power series. These results are then applied to the vector-like parameterization of Reissner–Simo beam theory, enabling a straightforward derivation and leading to a clearer Formulation. In particular, and in contrast with previous Formulations, a relatively compact and obviously symmetric form of the tangent operator is obtained. The paper also discusses several relevant issues concerning a beam finite element implementation and concludes with the presentation of a few selected illustrative examples. Copyright © 2002 John Wiley & Sons, Ltd.
Yusuf Yayli - One of the best experts on this subject based on the ideXlab platform.
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Some variations of dual Euler–Rodrigues Formula with an application to point–line geometry
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Derya Kahveci̇, Yusuf YayliAbstract:This paper examines the Euler-Rodrigues Formula in dual 3−space D 3 D 3 by analyisng its variations such as vectorial form, exponential map, point-line theory and quaternions which have some intrinsic relations. Contrary to the Euclidean case, dual rotation in dual 3−space corresponds to a screw motion in Euclidean 3−space. This paper begins by explaining dual motion in terms of the given dual axis and angle. It will then go on to express dual Euler-Rodrigues Formula with algebraic methods. Furthermore, an application of dual Euler-Rodrigues Formula to point-line geometry is accomplished and point-line displacement operator is obtained by dual Euler-Rodrigues Formula. Finally, dual Euler-Rodrigues Formula is presented with the help of dual Euler-Rodrigues parameters that is expressed as a dual quaternion.
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some variations of dual euler Rodrigues Formula with an application to point line geometry
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Derya Kahveci, Ismail Gok, Yusuf YayliAbstract:Abstract This paper examines the Euler–Rodrigues Formula in dual 3-space D 3 by analyzing its variations such as vectorial form, exponential map, point–line theory and quaternions which have some intrinsic relations. Contrary to the Euclidean case, dual rotation in dual 3-space corresponds to a screw motion in Euclidean 3-space. This paper begins by explaining dual motion in terms of the given dual axis and angle. It will then go on to express dual Euler–Rodrigues Formula with algebraic methods. Furthermore, an application of dual Euler–Rodrigues Formula to point–line geometry is accomplished and point–line displacement operator is obtained by dual Euler–Rodrigues Formula. Finally, dual Euler–Rodrigues Formula is presented with the help of dual Euler–Rodrigues parameters that is expressed as a dual quaternion.
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the geometrical and algebraic interpretations of euler Rodrigues Formula in minkowski 3 space
International Journal of Geometric Methods in Modern Physics, 2016Co-Authors: Derya Kahveci, Yusuf YayliAbstract:The aim of this paper is to give the geometrical and algebraic interpretations of Euler–Rodrigues Formula in Minkowski 3-space. First, for the given non-lightlike axis of a unit length in ℝ13 and angle, the spatial displacement is represented by a 3 × 3 semi-orthogonal rotation matrix using orthogonal projection. Second, we obtain the classifications of Euler–Rodrigues Formula in terms of semi-skew-symmetric matrix corresponds to spacelike, timelike or lightlike axis and rotation angle with the help of exponential map. Finally, an alternative method is given to find rotation axis and the Euler–Rodrigues Formula is expressed via split quaternions in Minkowski 3-space.
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The geometrical and algebraic interpretations of Euler–Rodrigues Formula in Minkowski 3-space
International Journal of Geometric Methods in Modern Physics, 2016Co-Authors: Derya Kahveci̇, Yusuf YayliAbstract:The aim of this paper is to give the geometrical and algebraic interpretations of Euler–Rodrigues Formula in Minkowski 3-space. First, for the given non-lightlike axis of a unit length in ℝ13 and angle, the spatial displacement is represented by a 3 × 3 semi-orthogonal rotation matrix using orthogonal projection. Second, we obtain the classifications of Euler–Rodrigues Formula in terms of semi-skew-symmetric matrix corresponds to spacelike, timelike or lightlike axis and rotation angle with the help of exponential map. Finally, an alternative method is given to find rotation axis and the Euler–Rodrigues Formula is expressed via split quaternions in Minkowski 3-space.
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FormulaS FOR THE EXPONENTIAL OF A SEMI SKEW- SYMMETRIC MATRIX OF ORDER 4
Mathematical & Computational Applications, 2005Co-Authors: Levent Kula, Murat Kemal Karacan, Yusuf YayliAbstract:In this paper the Formula of the exponential matrix e A when A is a semi skew-symmetric real matrix of order 4 is derived. The Formula is a generalization of the Rodrigues Formula for skew-symmetric matrices of order 3 in Minkowski 3-space.
Miki Wadati - One of the best experts on this subject based on the ideXlab platform.
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Rodrigues Formulas for the non-symmetric multivariable polynomials associated with the BCN-type root system
Nuclear Physics B, 2000Co-Authors: Akinori Nishino, Hideaki Ujino, Yasushi Komori, Miki WadatiAbstract:Abstract The non-symmetric Macdonald–Koornwinder polynomials are joint eigenfunctions of the commuting Cherednik operators which are constructed from the representation theory for the affine Hecke algebra corresponding to the BCN-type root system. We present the Rodrigues Formula for the non-symmetric Macdonald–Koornwinder polynomials. The raising operators are derived from the realizations of the corresponding double affine Hecke algebra. In the quasi-classical limit, the above theory reduces to that of the BCN-type Sutherland model which describes many particles with inverse-square long-range interactions on a circle with one impurity. We also present the Rodrigues Formula for the non-symmetric Jacobi polynomials of type BCN which are eigenstates of the BCN-type Sutherland model.
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Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
Journal of the Physical Society of Japan, 1999Co-Authors: Akinori Nishino, Hideaki Ujino, Miki WadatiAbstract:Extending a method developed by Takamura and Takano, we present the Rodrigues Formula for the nonsymmetric multivariable Laguerre polynomials which form the orthogonal basis for the $B_{N}$-type Calogero model with distinguishable particles. Our construction makes it possible for the first time to algebraically generate all the nonsymmetric multivariable Laguerre polynomials with different parities for each variable.Comment: 6 pages, LaTe
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Rodrigues Formula for the Nonsymmetric Macdonald Polynomial
Journal of the Physical Society of Japan, 1999Co-Authors: Akinori Nishino, Hideaki Ujino, Miki WadatiAbstract:Through the q -deformation of the method developed by Takamura and Takano for the nonsymmetric Jack polynomials, we present the Rodrigues Formula for the nonsymmetric Macdonald polynomials.
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Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
Journal of the Physical Society of Japan, 1999Co-Authors: Hideaki Ujino, Miki WadatiAbstract:Applying a method developed by Takamura and Takano for the nonsymmetric Jack polynomial, we present the Rodrigues Formula for the nonsymmetric multivariable Hermite polynomial.
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Rodrigues Formula for hi jack symmetric polynomials associated with the quantum calogero model
Journal of the Physical Society of Japan, 1996Co-Authors: Hideaki Ujino, Miki WadatiAbstract:The Hi-Jack symmetric polynomials, which are associated with the simultaneous eigenstates for the first and second conserved operators of the quantum Calogero model, are studied. Using the algebraic properties of the Dunkl operators for the model, we derive the Rodrigues Formula for the Hi-Jack symmetric polynomials. Some properties of the Hi-Jack polynomials and the relationships with the Jack symmetric polynomials and with the basis given by the QISM approach are presented. The Hi-Jack symmetric polynomials are strong candidates for the orthogonal basis of the quantum Calogero model.
Luc Vinet - One of the best experts on this subject based on the ideXlab platform.
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representations of the schrodinger group and matrix orthogonal polynomials
Journal of Physics A, 2011Co-Authors: Luc Vinet, Alexei ZhedanovAbstract:The representations of the Schrodinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable that have Charlier and Meixner polynomials as building blocks. The underlying Lie-theoretic framework allows for a systematic derivation of the structural Formulas (recurrence relations, difference equations, Rodrigues’ Formula, etc) that these matrix orthogonal polynomials satisfy.
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representations of the schr odinger group and matrix orthogonal polynomials
arXiv: Mathematical Physics, 2011Co-Authors: Luc Vinet, Alexei ZhedanovAbstract:The representations of the Schr\"odinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable that have Charlier and Meixner polynomials as building blocks. The underlying Lie-theoretic framework allows for a systematic derivation of the structural Formulas (recurrence relations, difference equations, Rodrigues' Formula etc.) that these matrix orthogonal polynomials satisfy.
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Rodrigues Formulas for the macdonald polynomials
arXiv: Quantum Algebra, 1996Co-Authors: Luc Lapointe, Luc VinetAbstract:We present Formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions through the repeated application of creation operators on the constant 1. Three expressions for the creation operators are derived one from the other. When the last of these expressions is used, the associated Rodrigues Formula readily implies the integrality of the (q,t)-Kostka coefficients. The proofs given in this paper rely on the connection between affine Hecke algebras and Macdonald polynomials
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a Rodrigues Formula for the jack polynomials and the macdonald stanley conjecture
arXiv: Quantum Algebra, 1995Co-Authors: Luc Lapointe, Luc VinetAbstract:A Formula of Rodrigues-type for the Jack polynomials is presented. It is seen to imply a weak form of a conjecture of Macdonald and Stanley.
