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In this paper, the spherical indicatrix curves drawn by quaternionic frenet vectors are computed. Also the quaternionic geodesic curvatures of the spherical indicatrix curves to E 3 and S 2 are found.

Topics: Real quaternion, Spatial quaternion, Indicatrix curve

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104

Nov 18, 2015
11/15

by
V. Christianto, F. Smarandache

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It is known that quaternion number has wide application in theoretical physics and engineering fields alike, in particular to describe Maxwell electrodynamics. In the meantime, recently this quaternion number has also been used to draw fractal graph. The present note is intended as an introduction to this very interesting study, i.e. to find linkage between quaternion/biquaternion number, quantum mechanical equation (Schrödinger equation) and fractal graph. Hopefully this note will be found...

Topics: energy, quaternion number

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99

Nov 18, 2015
11/15

by
V. Chrisitanto, F. Smarandache

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Despite incomparable achievement of Quantum Electrodynamics and its subsequent theories, there are some known limitations and unsolved theoretical problems until this time, including ‘renormalization’ condition and its generalization to larger systems.

Topics: Generalized Quaternion Quantum Electrodynamics, electrodynamics theories

In this study, new highly parallel algorithm of two-sided Jacobi 8-D transformation is suggested. It is oriented on VLSI-implementation of special processor array. This array is built using 8-D CORDIC algorithm for quaternion valued matrix singular value decomposition. Accuracy analysis and simulation results are added. Such array can be utilized to speed up the Jacobi method realization to compute the SVD of a quaternion matrix in signal and image processing.

Topics: Quaternion Matrix, Jacobi Method, SVD, Processor Arrays

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508

Nov 16, 2015
11/15

by
Vic Chrisitianto, Florentin Smarandache

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Quaternion space and its respective Quaternion Relativity (it also may be called as Rotational Relativity) has been defined in a number of papers, and it can be shown that this new theory is capable to describe relativistic motion in elegant and straightforward way. Nonetheless there are subsequent theoretical developments which remains an open question, for instance to derive Maxwell equations in Q-space. Therefore the purpose of the present paper is to derive a consistent description of...

Topics: Quaternion space, Maxwell equations, Lorentz force.

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40

Oct 21, 2019
10/19

by
Peter Michael Jack

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A unique method for solving quadratic equations over the skew field of quaternions is presented. It involves the novel two-hand quaternion approach, where the usual non-commuting products in the right-handed quaternion algebra can be effectively permuted by introducing the left-handed quaternion on the opposite side of the variables. This simple technique enables the manipulation of algebraic expressions, once thought too complicated to re-solve, into rather trivial manipulations, that often...

Topics: quaternion, quaternions, Hamilton, non-abelian algebra, quadratic equations

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56

Nov 16, 2015
11/15

by
Florentin Smarandache

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The following blogs on applications of neutrosophics and multispace in sciences include meditations / reflections on science, comments, hypotheses, proposals, comparisons of ideas, possible projects, extensions or deviations or alternatives to classical knowledge, etc. selected from e-mails, letters, drafts, conversations, impressions, my diary, etc.

Topics: non-standard quaternion space, non-standard biquaternion space

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197

Jul 7, 2018
07/18

by
Robert Edward Grant

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Published work of Robert E. Grant.

Topics: Number Theory, Math, Mathematics, Physics, Numbers, Patterns, Quadripolarity, Quaternion,...

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22

Feb 8, 2020
02/20

by
Kyrala, A

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xiii, 359 pages : 25 cm

Topics: Tensor, Vektorrechnung, Mathematical physics, Mathematische fysica, Wiskunde, Toepassingen,...

Magnetic, angular rate, and gravity (MARG) sensor modules have extensive applications in inertial navigation and motion tracking. A wide assortment of these sensor modules exist at varying cost points. In the current fiscal environment, affordable devices are needed; however, performance cannot be sacrificed. The main purpose of the study is to devise a series of tests to evaluate the dynamic accuracy of the LORD MicroStrain® 3DM-GX4-25 Attitude Heading Reference System (AHRS). Previous NPS...

Topics: magnetic, angular rate, and gravity, MARG, micro-electro-mechanical systems, MEMS, quaternion

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146

Jan 27, 2020
01/20

by
SWUS, SOVEREIGN WEALTH US, LEE JOSEPH COMMON, ARMY, DEFENSE, INTELLIGENCE, MILITARY, ADVANCED, PHYSICS, FREE ENERGY, UNITY, OVER, ZERO POINT, ENERGY, REALITY, FREE, CREATIVE, MIND,

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LT COL THOMAS E. BEARDEN U.S. Missle Defense Command BOOKS & INTERNAL DEFENSE INTELLIGENCE PAPPERS

Topics: SCALAR, QUATERNION, EQUASION, MAXWELL, INFEREOMETRY, PHENOMONOLOGY, UNIFIED THEORY, ETHICAL,...

The growth in smartphone usage has led to increased storage of sensitive data on these easily lost or stolen devices. In order to mitigate the effects of users who ignore, disable, or circumvent authentication measures like passwords, we evaluate a method employing gait as a source of identifying information. This research is based on previously reported methods with a goal of evaluating gait signal processing and classification techniques. This thesis evaluates the performance of four signal...

Topics: Smartphone authentication, accelerometer gait recognition, signal processing, quaternion rotation,...

The purpose of this paper is to locate and estimate the eigen values of quaternion doubly stochastic matrices. We present several estimation theorems about the eigen values of quaternion doubly stochastic matrices. Mean while, we obtain the distribution theorem for the eigen values of tensor products of two quaternion doubly stochastic matrices. We will conclude the paper with the distribution for the eigen values of generalized quaternion doubly stochastic matrices. by Dr. Gunasekaran K |...

Topics: Quaternion doubly stochastic matrices, Eigen values and tensor product, gerschgorin balls. AMS...

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58

May 6, 2016
05/16

by
IJOER Engineering journal

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In this study, we introduce quaternionic type-2 Harmonic Curvatures and General Helices according to Frenet frame in 4-dimensional Euclidean Space and investigate its properties for two cases. In the first case; we use a constant angle between a unit and fixed direction vector field and the first relatively Frenet frame vector field of the curve, that is, where is the real quaternion inner product. Since the relatively Frenet frame vector field of the curve makes a...

Topics: Euclidean spaces, General helix, type-2 harmonic curvatures, Quaternion algebra, Quaternionic...

This work describes the development and testing of a personal navigation system (PNS) for use during normal walking on level ground surfaces. A shoe-worn miniature inertial/magnetic measurement unit (IMMU), which is comprised of accelerometers, magnetometers, and angular rate sensors, provides the measurement data for the PNS algorithm. The well-known strapdown navigation algorithm is adapted for use in the PNS, which further incorporates the error correction technique commonly referred to as...

Topics: Inertial navigation., personal navigation, accelerometer, magnetometer, angular rate sensor,...

In this thesis, an open-architecture control moment gyroscope (CMG) system is developed for hardware-in-the-loop (HIL) simulation of spacecraft attitude control. This effort included construction of four single-gimbal CMGs, implementation of an attitude dynamics model, a quaternion error feedback control system, and a pseudoinverse CMG steering law on a real-time controller. The modular design of the embedded flight computer software allows for various parameters (such as the spacecraft inertia...

Topics: control moment gyroscopes, spacecraft attitude controls, hardware-in-the-loop simulation, real-time...

LibriVox recording of Short Nonfiction Collection, Vol. 073 by Various. Read by LibriVox Volunteers Twenty short nonfiction works chosen by the readers. "Salve! ye dumb hearts. Let us be still and wait by the roadside." With these words, Kate Chopin decries the "crushing feet, the clashing discords, the ruthless hands and stifling breath” that power the “mad pace" of everyday life. Broadway: the Backbone of New York presents a more up-beat view of city life. Reflections...

Topics: librivox, audiobooks, Japan, mathematics, Friendship, plague, inca, hawaii, galsworthy, poland,...

In close quarters combat, the lack of situational awareness can cause confusion, limit tempo of operations, and lead to fratricide. One approach to enhance the small-unit leader's situational awareness is to develop a network capable of mapping friendly positions. Current techniques for tracking the individual rifleman rely heavily on GPS, which does not work well indoors where satellite coverage is limited or even non-existent. One solution is to use inertial navigation systems to augment...

Topics: Personal navigation system, rotation matrix, geometry of fire, situational awareness, close...

The continuous cycle for validating geometry of fires on a battlefield impedes momentum. A force that can decide and act quicker than the enemy has an advantage. The goal of this thesis is to provide dismounted infantry units with this advantage by developing a sensor network that streamlines the geometry-of-fire validation cycle for direct-fire weapon systems. This is the first attempt to develop technology for this specific application. Prototyping the system’s overall design became this...

Topics: Geometry of fire, situational awareness, close quarters combat, direct-fire weapon system, tactical...

From the bitsavers.org collection, a scanned-in computer-related document. mit :: ai :: aim :: AIM-994

Topics: baseline, orientation, rotation, relative, perpendicular, rays, equation, corresponding, unit,...

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666

Feb 16, 2009
02/09

by
Peter Guthrie Tait

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Book digitized by Google from the library of Ghent University and uploaded to the Internet Archive by user tpb.

Topics: equation, vector, plane, perpendicular, vectors, quaternion, scalar, equations, parallel, tangent,...

Source: http://books.google.com/books?id=PCYPAAAAQAAJ&oe=UTF-8

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1.7K

Sep 7, 2008
09/08

by
Alexander Macfarlane

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Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

Topics: der, des, sur, die, ueber, von, quaternions, dublin, und, quaternion, ueber die, sur les, theorie...

Source: http://books.google.com/books?id=CkE6AAAAMAAJ&oe=UTF-8

A six degree of freedom, 20-state model of two spacecraft rendezvous is developed, one of which was controlled and the other considered to be passively tumbling. Solutions that minimize a series of performance indices are obtained for the problem of close approach, up to the point of contact, using a direct optimal control method. The solution is then verified as optimal by way of an indirect method based on the Minimum Principle. Next, a trajectory generation method for spacecraft...

Topics: Space trajectories., spacecraft proximity operations, Inverse Dynamics in the Virtual Domain,...

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424

Jul 10, 2008
07/08

by
Peter Guthrie Tait

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: equation, vector, plane, perpendicular, vectors, quaternion, scalar, parallel, equations, tangent,...

Source: http://books.google.com/books?id=PpIKAAAAYAAJ&oe=UTF-8

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3.0

Aug 12, 2020
08/20

by
Altmann, Simon L., 1924-

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xiv, 317 pages : 24 cm

Topics: Rotation groups, Quaternions, Finite groups, Representations of groups, Groupe double, Groupe,...

From the bitsavers.org collection, a scanned-in computer-related document. mit :: ai :: aim :: AIM-806

Topics: configuration, constraints, object, quaternion, edge, rotation, constraint, type, vertex, space,...

The use of inertial-measurement units (IMUs) for personal navigation is investigated in this thesis. IMUs lack a position-finding algorithm that optimally blends sensor data to achieve high accuracy in a GPS-denied environment. In this research, software and a methodology for tracking position using body-mounted IMUs, building on a gait-phase detection algorithm and quaternion-based complementary filter developed at the Naval Postgraduate School, is developed. The performance of a...

Topics: personal navigation, inertial sensor, gyroscope, magnetometer, accelerometer, attitude heading and...