Quaternions and Rotation Sequences (eBook)

A Primer with Applications to Orbits, Aerospace and Virtual Reality

J. B. Kuipers (Autor)

eBook Download: PDF

2020
400 Seiten
Princeton University Press (Verlag)
978-0-691-21170-1 (ISBN)

Infos

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations. The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.

Produkt-Details

• Erscheint lt. Verlag: 31.3.2020
• Zusatzinfo: 121 figures
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Schlagworte: adjoint equation • Aircraft • algorithm • Angle of rotation • angles • angular frequency • angular velocity • Axonometric projection • Basis (linear algebra) • Canonical transformation • Cartesian coordinate system • Celestial mechanics • Center of mass (relativistic) • Central angle • Circular Orbit • clockwise • commutative property • complex number • complex numbers • Computation • Conjugate transpose • coordinate frame • coordinate system • coupling • Cramer's Rule • Determinant • differential equation • Dimension • direction cosine • Direction vector • Division Ring • Divisor • dot product • Eigenvalues and Eigenvectors • Electromagnetic • ephemeris • Equation • Euclidean Vector • Euler angle • Euler angles • Euler sequence • Factor • Factorization • Geographic coordinate system • geometric transformation • Geometry • great-circle • Homogeneous Coordinates • Hypercomplex number • Identity • Identity matrix • incremental rotation • integral domain • Internal and external angles • inverse • Invertible matrix • isometric projection • linear algebra • linear differential equation • Linear Function • Mathematical Induction • Matrix • matrix analysis • Matrix differential equation • matrix multiplication • Multiplicative Inverse • Norm (mathematics) • Notation • Number • Operator algebra • Orbit • Orbital elements • orientation • orthogonal matrix • Orthonormal basis • Orthonormality • Parallel (geometry) • parallel postulate • Parallel projection • Perspective • phase plane • Phase space • Planar projection • Polar representation • projection • Quadrilateral • quaternion • Quaternion Algebra • Radial line • Radian • real number • Rotation • Rotation (mathematics) • Rotation Matrix • Rotation operator • Rotation operator (quantum mechanics) • Row and column vectors • Seasons • Semi-major and semi-minor axes • Sequence • Simultaneous Equations • Space partitioning • Sphere • spherical • Spherical Coordinate System • Spherical trigonometry • Summation • Tangent Space • Trace (linear algebra) • trace of a matrix • transformation matrix • Translation operator (quantum mechanics) • transpose • Trigonometry • two-dimensional space • Unit sphere • Unit vector • Vector Algebra • Vector notation • Vector Space • Velocity • Virtual Reality
• ISBN-10: 0-691-21170-1 / 0691211701
• ISBN-13: 978-0-691-21170-1 / 9780691211701