Bookcover of Monomial (1,0,-1) – Matrices – (4x4)
Booktitle:

Monomial (1,0,-1) – Matrices – (4x4)

Part 2 Application to the Rotation in Space

LAP LAMBERT Academic Publishing (2017-06-22 )

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ISBN-13:

978-3-330-34185-2

ISBN-10:
3330341858
EAN:
9783330341852
Book language:
English
Blurb/Shorttext:
A special mathematical apparatus for monomial (1,0,-1)–matrices–(4×4) is applied to the description of kinematics and kinetics of rotation in space of an asymmetric rigid body about a fixed point. Using matrix representations for vector operations, Rodrigues vector formula is converted to concise, ordered record in quaternionic matrices. Using transposition operations, forward and indirect coordinate transformations’ matrices when rotating in space are represented by a commutative matrix compositions formed by Rodrigues-Hamilton parameters. The universal algorithm for coordinate transformation matrices formation is offered for an arbitrary sequence of independent rotations. This algorithm was tested on a set of three independent rotations’ systems and their connection with Gibbs vector components was established. Using quaternionic matrices’ properties there were derived invariants of angular velocity, kinetic energy, inertia matrix when rotating. The formulas for time differentiation of vector-function (hodograph), second rank tensor (inertia matrix) in the absolute and local reference systems are represented by equivalent record in quaternionic matrices.
Publishing house:
LAP LAMBERT Academic Publishing
Website:
https://www.lap-publishing.com/
By (author) :
Victor Kravets, Tamila Kravets, Olexiy Burov
Number of pages:
92
Published at:
2017-06-22
Stock:
Available
Category:
Mechanical engineering, manufacturing technology
Price:
39.90 €
Keywords:
0, kinematics, kinetics, quaternionic matrices, Rockets, rotation in space, monomial (1, -1)-matrices-(4x4), parameters of Rodrigues-Hamilton, finite rotation, Gibbs vector

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