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Relevant bibliographies by topics / Quaternions and vector analysis

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Academic literature on the topic 'Quaternions and vector analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Quaternions and vector analysis"

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Mansouri, Imed, and Mohammed Ouali. "QUATERNION REPRESENTATION OF THE POWER MANIPULABILITY." Transactions of the Canadian Society for Mechanical Engineering 35, no. 2 (2011): 309–36. http://dx.doi.org/10.1139/tcsme-2011-0018.

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In this paper, a quaternion formulation of the power manipulability is developed. Quantifying the mechanical transmissibility of a mechanism, this parameter was previously introduced as a new homogeneous performance index of robot manipulators; however, its evaluation requires complex manipulations, particularly those of quadri-vectors. Furthermore, the quadri-vector form fits exactly with the structure of quaternions. Hence, a quaternion based method may be useful for power performance indices evaluation. It will be shown that this method leads to a recursive algorithm that manipulates kinema

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Cho, Ilwoo, and Palle E. T. Jorgensen. "Multi-variable quaternionic spectral analysis." Opuscula Mathematica 41, no. 3 (2021): 335–79. http://dx.doi.org/10.7494/opmath.2021.41.3.335.

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In this paper, we consider finite dimensional vector spaces \(\mathbb{H}^n\) over the ring \(\mathbb{H}\) of all quaternions. In particular, we are interested in certain functions acting on \(\mathbb{H}^n\), and corresponding functional equations. Our main results show that (i) all quaternions of \(\mathbb{H}\) are classified by the spectra of their realizations under representation, (ii) all vectors of \(\mathbb{H}^n\) are classified by a canonical extended setting of (i), and (iii) the usual spectral analysis on the matricial ring \(M_n(\mathbb{C})\) of all \((n \times n)\)-matrices over the

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Li, Guozhi, Fuhai Zhang, Yili Fu, and Shuguo Wang. "Kinematic calibration of serial robot using dual quaternions." Industrial Robot: the international journal of robotics research and application 46, no. 2 (2019): 247–58. http://dx.doi.org/10.1108/ir-10-2018-0221.

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Purpose The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions. Design/methodology/approach The dual quaternions are the combination of dual-number theory and quaternion algebra, which means that they can represent spatial transformation. The dual quaternions can represent the screw displacement in a compact and efficient way, so that they are used for the kinematic analysis of serial robot. The error model proposed in this paper is derived from the forward kinematic equations via using dual quaternion algebra. The full pose meas

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Weng, Zi-Hua. "Forces in the complex octonion curved space." International Journal of Geometric Methods in Modern Physics 13, no. 06 (2016): 1650076. http://dx.doi.org/10.1142/s0219887816500766.

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The paper aims to extend major equations in the electromagnetic and gravitational theories from the flat space into the complex octonion curved space. Maxwell applied simultaneously the quaternion analysis and vector terminology to describe the electromagnetic theory. It inspires subsequent scholars to study the electromagnetic and gravitational theories with the complex quaternions/octonions. Furthermore Einstein was the first to depict the gravitational theory by means of tensor analysis and curved four-space–time. Nowadays some scholars investigate the electromagnetic and gravitational prop

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de Farias, Cristiana Miranda. "A Novel Dual Quaternion Based Cost Effcient Recursive Newton-Euler Inverse Dynamics Algorithm." International Journal of Robotic Computing 1, no. 2 (2019): 144–68. http://dx.doi.org/10.35708/rc1868-126255.

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In this paper, the well known recursive Newton-Euler inverse dynamics algorithm for serial manipulators is reformulated into the context of the algebra of Dual Quaternions. Here we structure the forward kinematic description with screws and line displacements rather than the well established Denavit-Hartemberg parameters, thus accounting better efficiency, compactness and simpler dynamical models. We also present here the closed solution for the dqRNEA, and to do so we formalize some of the algebra for dual quaternion-vectors and dual quaternion-matrices. With a closed formulation of the dqRNE

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Hu, Xing Zhi, Xiao Qian Chen, and Yong Zhao. "Coordinate Transform Methods Used in Dynamic Simulation of Satellite Separation." Advanced Materials Research 569 (September 2012): 712–17. http://dx.doi.org/10.4028/www.scientific.net/amr.569.712.

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Direction cosine matrix, Euler angles and quaternions are the common methods for translating vector equations into scalar equations. These methods used in separation simulation lack systematic discussion and comparison. This article is trying to present a proper coordinate transformation method for dynamic analysis of satellite separation. 321 and 123 rotations of Euler angles are proposed to construct the dynamic equations, which is different from simulation of missiles by the rotation of 321 and 231. Both Euler angles and quaternions are adopted to model the separation process of a small sat

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Shi, Xiaoping, Xuan Peng, and Yupeng Gong. "Immersion and Invariance Adaptive Control for Spacecraft Pose Tracking via Dual Quaternions." Complexity 2021 (April 15, 2021): 1–18. http://dx.doi.org/10.1155/2021/6624222.

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This paper addresses the simultaneous attitude and position tracking of a target spacecraft in the presence of general unknown bounded disturbances in the framework of dual quaternions, which provides a concise and integrated description of the coupled rotational and translational motions. By virtue of the newly introduced dual direction cosine matrix, the dimension of the dual quaternion-based relative motion dynamics written in vector/matrix form can be lowered to six. Treating the disturbances as unknown parameters, a modular adaptive pose tracking control scheme composed of two separately

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Cho, Ilwoo. "Certain nonlinear functions acting on the vector space H^n over the Quaternions H." Journal of Nonlinear Sciences and Applications 15, no. 01 (2021): 14–40. http://dx.doi.org/10.22436/jnsa.015.01.02.

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RAJA, M., Ugur GUVEN, and Kartikay SINGH. "Design and Implementation of a 3-Dimensional Attitudes Estimator Device using Low Cost Accelerometer & Gyroscope with Microcontroller IDE." INCAS BULLETIN 12, no. 2 (2020): 151–61. http://dx.doi.org/10.13111/2066-8201.2020.12.2.13.

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Navigation and guidance systems for most automobile as well as aerospace applications require a coupled chip setup known as Inertial Measurement Units (IMU) which, depending on the degree of freedoms, contains a Gyroscope (for maintaining orientation and angular velocity), Accelerometers (to determine acceleration in the respective direction) and a Magnetometer (to determine the respective magnetic fields). In the three-dimensional space, any required rotation analysis is limited to the coordinate systems and all subtended angles in either direction must be defined by a fixed axis to effective

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NG, CHI-KEUNG. "On quaternionic functional analysis." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 2 (2007): 391–406. http://dx.doi.org/10.1017/s0305004107000187.

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AbstractIn this paper, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion B*-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real C*-algebras respectively. We will also give a Riesz representation theorem for quaternion Hilbert spaces and will extend the main results in [12] (namely, we will give the full versions of the Gelfand–Naimark theorem and the Gelfand theorem for quaternion B*-algebras). On our way to th

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Dissertations / Theses on the topic "Quaternions and vector analysis"

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Bushman, Nathan. "Hypercomplex Numbers and Early Vector Systems: A History." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1585666516546138.

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Resende, Adriana Souza. "Introdução elementar às álgebras Clifford 'CL IND.2' 'CL IND. 3'." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306698.

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Orientador: Waldyr Alves Rodrigues Junior<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-15T23:09:32Z (GMT). No. of bitstreams: 1 Resende_AdrianaSouza_M.pdf: 17553204 bytes, checksum: a66cefe30e9957cc4351e03d3aec35b2 (MD5) Previous issue date: 2010<br>Resumo: O presente trabalho tem a intenção de apresentar por intermédio de uma linguagem unificada alguns conceitos de cálculo vetorial, álgebra linear (matrizes e transformações lineares) e também algumas idéias elem

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Whelchel, Pamela Jean. "Analysis on a hyperplane of the quaternions." CSUSB ScholarWorks, 1995. https://scholarworks.lib.csusb.edu/etd-project/1221.

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Gezgin, Erkin Alizade Rasim. "Biokinematic analysis of human arm." [s.l.]: [s.n.], 2006. http://library.iyte.edu.tr/tezler/master/makinamuh/T000547.pdf.

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Thesis (Master)--İzmir Institute of Technology, İzmir, 2006.<br>Keywords: Biokinematic analysis, quaternionlar, structural groups, mechanism theory,robot manipulators. Includes bibliographical references (leaves 78-85).

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Aparicio, Conrado. "Implementation of a quaternion-based Kalman filter for human body motion tracking using MARG sensors." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2004. http://library.nps.navy.mil/uhtbin/hyperion/04Sep%5FAparicio.pdf.

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Polito, Vito. "Vector autoregressive analysis of macroeconomic policy." Thesis, University of York, 2007. http://etheses.whiterose.ac.uk/11068/.

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Sinav, Alper. "Analysis and modeling of the virtual human interface for the MARG body tracking system using quaternions." Thesis, Monterey, California. Naval Postgraduate School, 2002. http://hdl.handle.net/10945/6018.

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Approved for public release; distribution unlimited<br>This thesis done in cooperation with the MOVES Institute<br>Mathematicians have used quaternions for about a hundred years. Today they are an important part of computer graphics and simulation systems. This thesis takes an analytical approach to quaternions by using them in the construction of a virtual human for sourceless Magnetic Accelerometer Rate Sensor (MARG) body tracking system. Virtual citizens will be a reflection of our personalities in cyberspace. Prophecies say they may take control in the virtual world and govern themselves t

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Kumar, Indra E. "Graphical Applications of Complex and Quaternionic Fractional Linear Transformations." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/scripps_theses/888.

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The geometric properties of the complex numbers and the quaternions, particularly their behavior under fractional linear transformations, make them very useful for modeling certain types of geometric objects. In this thesis, we will connect the characteristics of fractional linear transformations of both the complex numbers and quaternions to the problem of developing and modifying discrete surfaces for problems in computer graphics and engineering.

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Dussault, Serge. "Nonlinear seismic analysis using vector superposition methods." Thesis, McGill University, 1991. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60575.

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This thesis presents two algorithms to solve nonlinear seismic problems in generalized coordinates, one that uses a set of vectors computed from initial properties, the Pseudo-Force Method (PFM), and another that continuously updates the vector basis to represent the nonlinear behaviour, the Tangent Spectrum Method (TSM). Both methods can use either exact eigenvectors or load dependent vectors as vector basis. Parametric analyses are carried out on a series of multistory buildings idealized as shear beam structures with bilinear hysteretic behaviour. The effects of the truncation of the vector

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Claesson, Kenji. "Implementation and Validation of Independent Vector Analysis." Thesis, Umeå University, Physics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-32306.

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<p>This Master’s Thesis was part of the project called Multimodalanalysis at the Depart-ment of Biomedical Engineering and Informatics at the Ume˚ University Hospital inUme˚ Sweden. The aim of the project is to develop multivariate measurement anda,analysis methods of the skeletal muscle physiology. One of the methods used to scanthe muscle is functional ultrasound. In a study performed by the project group datawas aquired, where test subjects were instructed to follow a certain exercise scheme,which was measured. Since there currently is no superior method to analyze the result-ing data (in f

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Books on the topic "Quaternions and vector analysis"

1

Freguglia, Paolo. Dalle equipollenze ai sistemi lineari: Il contributo italiano al calcolo geometrico. QuattroVenti, 1992.

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J, Booth Dexter, ed. Vector analysis. Industrial Press, 2005.

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Vector analysis. Springer, 2001.

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Louis, Brand. Vector analysis. Dover Publications, 2006.

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Jänich, Klaus. Vector Analysis. Springer New York, 2001.

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Jänich, Klaus. Vector Analysis. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3478-2.

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Galbis, Antonio, and Manuel Maestre. Vector Analysis Versus Vector Calculus. Springer US, 2012. http://dx.doi.org/10.1007/978-1-4614-2200-6.

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Galbis, Antonio. Vector Analysis Versus Vector Calculus. Springer US, 2012.

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Eisenman, Richard. Matrix vector analysis. Dover Publications, 2005.

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Rahman, M. Applied vector analysis. 2nd ed. CRC Press, 2008.

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Book chapters on the topic "Quaternions and vector analysis"

1

Kantor, I. L., and A. S. Solodovnikov. "Quaternions and Vector Algebra." In Hypercomplex Numbers. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3650-4_4.

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Glaeser, Georg. "Vector analysis." In Math Tools. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66960-1_5.

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Råde, Lennart, and Bertil Westergren. "Vector Analysis." In Mathematics Handbook. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03556-6_11.

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Hassani, Sadri. "Vector Analysis." In Mathematical Methods. Springer New York, 2000. http://dx.doi.org/10.1007/978-0-387-21562-4_8.

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Romano, Antonio, and Addolorata Marasco. "Vector Analysis." In Continuum Mechanics using Mathematica®. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1604-7_2.

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Parton, J. E., S. J. T. Owen, and M. S. Raven. "Vector Analysis." In Applied Electromagnetics. Macmillan Education UK, 1986. http://dx.doi.org/10.1007/978-1-349-18056-1_1.

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Oates, Gordon C. "Vector Analysis." In Handbook of Applied Mathematics. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-1423-3_3.

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Soon, Frederick H. "Vector Analysis." In Student’s Guide to Calculus by J. Marsden and A. Weinstein. Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4970-2_7.

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Parton, J. E., S. J. T. Owen, and M. S. Raven. "Vector Analysis." In Applied Electromagnetics. Springer US, 1986. http://dx.doi.org/10.1007/978-1-4684-0618-4_1.

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Harris, John W., and Horst Stocker. "Vector analysis." In Handbook of Mathematics and Computational Science. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-5317-4_16.

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Conference papers on the topic "Quaternions and vector analysis"

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Via, Javier, Luis Vielva, Ignacio Santamaria, and Daniel P. Palomar. "Independent component analysis of quaternion Gaussian vectors." In 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM). IEEE, 2010. http://dx.doi.org/10.1109/sam.2010.5606718.

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Miron, S., N. Le Bihan, and J. I. Mars. "High resolution vector-sensor array processing using quaternions." In 2005 Microwave Electronics: Measurements, Identification, Applications. IEEE, 2005. http://dx.doi.org/10.1109/ssp.2005.1628725.

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Grandi, A., A. Mazzotti, and E. Stucchi. "Multicomponent Velocity Analysis with Quaternions." In 69th EAGE Conference and Exhibition incorporating SPE EUROPEC 2007. European Association of Geoscientists & Engineers, 2007. http://dx.doi.org/10.3997/2214-4609.201401474.

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Bar-Itzhack, Itzhack, and Richard Harman. "An Algorithm for Optimal Fusion of Quaternions with Vector Measurements." In AIAA/AAS Astrodynamics Specialist Conference and Exhibit. American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-4830.

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Barry, Noel. "Electrical motor force analysis using quaternions." In 2015 50th International Universities Power Engineering Conference (UPEC). IEEE, 2015. http://dx.doi.org/10.1109/upec.2015.7339974.

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Brasil, Victor do Prado, Anesio de Leles Ferreira Filho, and Joao Yoshiyuki Ishihara. "Electrical three phase circuit analysis using quaternions." In 2018 18th International Conference on Harmonics and Quality of Power (ICHQP). IEEE, 2018. http://dx.doi.org/10.1109/ichqp.2018.8378813.

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Chen, Chih-Hsin, and Hong-Jian Chen. "Motion Representation: Different Conventional Forms, Duplex Mapping and Conjugation Form." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0392.

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Abstract Four fundamental forms for representing rigid body motion, i.e. the rotation-of-vector form, the matrix form, the quaternion form and the screw form, all based on the conventional concept that motion is specified by the movement of a reference point together with an orientation change, are expounded. The inter-relationships among these forms are elucidated. The geometric images of these representation-forms, i.e. the motion mappings, are explained, and an innovative duplex-mapping, a powerful tool for mobility analysis of multi-loop mechanisms and robots, is introduced. An exotic moti

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Terze, Zdravko, Andreas Mueller, and Dario Zlatar. "Redundancy-Free Integration of Rotational Quaternions in Minimal Form." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35118.

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Redundancy-free computational procedure for solving dynamics of rigid body by using quaternions as the rotational kinematic parameters will be presented in the paper. On the contrary to the standard algorithm that is based on redundant DAE-formulation of rotational dynamics of rigid body that includes algebraic equation of quaternions’ unit-length that has to be solved during marching-in-time, the proposed method will be based on the integration of a local rotational vector in the minimal form at the Lie-algebra level of the SO(3) rotational group during every integration step. After local rot

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Li-Hong Qiao, Wei Guo, Wei-Tao Yuan, Kai-Fu Niu, and Li-Zhong Peng. "Texture analysis based on Bidimensional Empirical Mode Decomposition and quaternions." In 2009 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR). IEEE, 2009. http://dx.doi.org/10.1109/icwapr.2009.5207477.

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Pinotsis, D. A. "Segre quaternions, spectral analysis and a four-dimensional Laplace equation." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_0032.

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Reports on the topic "Quaternions and vector analysis"

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Ott, R. H. Vector Analysis and Satellite Footprints. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada169832.

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Qin, H., W. M. Tang, and G. Rewoldt. Symbolic Vector Analysis in Plasma Physics. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/293439.

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Qin, H., G. Rewoldt, and W. M. Tang. Symbolic Vector Analysis in Plasma Physics. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/3677.

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Calahan, D. A., and D. H. Bailey. Measurement and Analysis of Memory Conflicts on Vector Multiprocessors. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada188206.

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Buscaino, B. Trend Analysis in Biomedical Texts via Vector Space Model Synonym Extraction. Office of Scientific and Technical Information (OSTI), 2014. http://dx.doi.org/10.2172/1165794.

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Miller, H. V., S. D. Coughlan, Kevin B. Shaw, and Susan V. Carter. Digital Mapping Charting and Geodesy Analysis Program Technical Review Vector Product Format (VPF). Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada289766.

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Ort, Sara E., and Carol A. Subick. The Analysis of Engineer Activity in the Vector-in-Commander (VIC) battle Simulation. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada273460.

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Bhatia, Harsh. Consistent Feature Extraction From Vector Fields: Combinatorial Representations and Analysis Under Local Reference Frames. Office of Scientific and Technical Information (OSTI), 2015. http://dx.doi.org/10.2172/1341967.

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Mokaya, Fridah. High Statistics Analysis of All-Neutral Decays of Vector Mesons with the Radphi Experiment. Office of Scientific and Technical Information (OSTI), 2018. http://dx.doi.org/10.2172/1574214.

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McAdams, H. T. A Vector Approach to Regression Analysis and Its Implications to Heavy-Duty Diesel Emissions. Office of Scientific and Technical Information (OSTI), 2001. http://dx.doi.org/10.2172/777660.

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