Results 41 to 50 of about 10,739 (275)
Dual-Quaternion-Based SLERP MPC Local Controller for Safe Self-Driving of Robotic Wheelchairs
Robotics, 2023 In this work, the motion control of a robotic wheelchair to achieve safe and intelligent movement in an unknown scenario is proposed. The primary objective is to develop a comprehensive framework for a robotic wheelchair that combines a global path ...
Daifeng Wang +2 more
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Quaternionic and Dual Quaternionic Darboux Ruled Surfaces
Turkish Journal of Mathematics and Computer Science, 2021 In this paper, firstly the ruled surface drawn by the Darboux vector is expressed as a quaternion. Then, the spatial quaternionic definition of the striction curve is given and the integral invariants of the surface are calculated. Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of ...
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Sextonians and the magic square [PDF]
, 2004 Associated to any complex simple Lie algebra is a non-reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and ...
Westbury, Bruce
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A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions
Mathematics, 2023 This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided for the 6-DOF differential equation of motion in the arbitrary non-inertial reference ...
Daniel Condurache
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Dual third-order Jacobsthal quaternions [PDF]
Proyecciones (Antofagasta), 2018 In 2016, Yüce and Torunbalcı Aydın (18) defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jacobsthal-Lucas quaternions. Also, we investigated the relations between the dual third-order Jacobsthal quaternions and third-order Jacobsthal numbers.
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Dual bicomplex Horadam quaternions [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 The aim of this work is to introduce a generalization of dual quaternions called dual bicomplex Horadam quaternions and to present some properties, the Binet’s formula, Catalan’s identity, Cassini’s identity and the summation formula for this type of bicomplex quaternions.
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, 2012 4-dimensional $F_{4} $ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(F_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions.
Catalan E. +14 more
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On the semicircular law of large dimensional random quaternion matrices [PDF]
, 2015 It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices.
Bai, Zhidong, Hu, Jiang, Yin, Yanqing
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The Kinematic Image of 2R Dyads and Exact Synthesis of 5R Linkages
, 2015 We characterise the kinematic image of the constraint variety of a 2R dyad as a regular ruled quadric in a 3-space that contains a "null quadrilateral". Three prescribed poses determine, in general, two such quadrics.
Rad, Tudor-Dan, Schröcker, Hans-Peter
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Quaternion modeling of the helical path for analysis of the shape of the DNA molecule
Вавиловский журнал генетики и селекции, 2018 The threedimensional shape of a DNA molecule is a key property influencing its functional specificity and the nature of its molecular interactions. The characteristic shape into which a DNA molecule folds under certain conditions is a manifestation of ...
A. F. Muterko
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