Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality
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 application...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2020]
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| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UER01 UPA01 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 05. Mai 2020) |
| Beschreibung: | 1 online resource 121 figures |
| ISBN: | 9780691211701 |
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| 520 | |a 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 | ||
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| 650 | 4 | |a perspective | |
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| 650 | 4 | |a quaternion | |
| 650 | 4 | |a rotation | |
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| author | Kuipers, Jack B. 1921- |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| isbn | 9780691211701 |
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| spelling | Kuipers, Jack B. 1921- Verfasser (DE-588)173306691 aut Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality J. B. Kuipers Princeton, NJ Princeton University Press [2020] © 1999 1 online resource 121 figures txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher's Web site, viewed 05. Mai 2020) 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 In English Euler angle aircraft algorithm angles complex numbers coordinate frame coupling direction cosine electromagnetic factor geometry great-circle homogeneous coordinates identity incremental rotation inverse matrix number orientation perspective phase plane projection quaternion rotation seasons spherical trace of a matrix virtual reality MATHEMATICS / Applied bisacsh Quaternions https://www.degruyter.com/isbn/9780691211701 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kuipers, Jack B. 1921- Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality Euler angle aircraft algorithm angles complex numbers coordinate frame coupling direction cosine electromagnetic factor geometry great-circle homogeneous coordinates identity incremental rotation inverse matrix number orientation perspective phase plane projection quaternion rotation seasons spherical trace of a matrix virtual reality MATHEMATICS / Applied bisacsh Quaternions |
| title | Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality |
| title_auth | Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality |
| title_exact_search | Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality |
| title_exact_search_txtP | Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality |
| title_full | Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality J. B. Kuipers |
| title_fullStr | Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality J. B. Kuipers |
| title_full_unstemmed | Quaternions and Rotation Sequences A Primer with Applications to Orbits, Aerospace and Virtual Reality J. B. Kuipers |
| title_short | Quaternions and Rotation Sequences |
| title_sort | quaternions and rotation sequences a primer with applications to orbits aerospace and virtual reality |
| title_sub | A Primer with Applications to Orbits, Aerospace and Virtual Reality |
| topic | Euler angle aircraft algorithm angles complex numbers coordinate frame coupling direction cosine electromagnetic factor geometry great-circle homogeneous coordinates identity incremental rotation inverse matrix number orientation perspective phase plane projection quaternion rotation seasons spherical trace of a matrix virtual reality MATHEMATICS / Applied bisacsh Quaternions |
| topic_facet | Euler angle aircraft algorithm angles complex numbers coordinate frame coupling direction cosine electromagnetic factor geometry great-circle homogeneous coordinates identity incremental rotation inverse matrix number orientation perspective phase plane projection quaternion rotation seasons spherical trace of a matrix virtual reality MATHEMATICS / Applied Quaternions |
| url | https://www.degruyter.com/isbn/9780691211701 |
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