## Geometry of Rotation: Understanding the Dynamics of Rigid Bodies

### Cornel Rigby; Cornel Rigby

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To fulfil the need for a suitable mathematical language, Geometry of Rotation presents: chapter 1 on vector algebra, chapter 2 on the algebra of dyadics and chapter 3 on transformations, invariance and the calculus of vectors and dyadics. Geometry of Rotation presents a new comprehensive theory on rigid body angular displacement. Chapter 4 introduces the concepts of the rotation vector and the rotation dyadic for simple rotations (about a fixed direction). Chapter 5 begins with a set of three experiments on finite successive rotations of a rigid body and ends with a presentation of the Euler angles as three properly defined finite successive rotations. Chapter 6 presents rigid body angular displacement theory in vector-dyadic language. The rotation vector emerges as the vector embedded in the rotation dyadic with several remarkable and very useful properties. Formulas are obtained for the resultant rotation vector of two and of three successive finite rotations.

Geometry of Rotation incorporates this angular displacement theory and presents an up-to-date, comprehensive theory of the kinematics of rigid bodies. Chapter 7 presents the kinematic problem of the rotation of a rigid body about a fixed point and proof that the angular velocity vector is the time derivative of the rotation vector. In chapter 8, the concepts of the rotation vector, the rotation dyadic and the angular velocity vector are generalized to cases of rigid bodies in relative rotational motion. Chapter 8 includes the derivation of formulas for the composition of the kinematic state vectors for multi-body systems of rigid bodies coupled at points to each other. Finally, chapter 9, presents the case of the general motion of the unconstrained rigid body, cases of generally coupled rigid bodies in general motion, and a complete set of extendable self-consistent kinematic state vector equations for generally coupled multi-body systems.

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From the Publisher:

Cornel Rigby’s new book Geometry of Rotation: Understanding the Dynamics of Rigid Bodies updates the core discipline of classical mechanics and presents it as a modern engineering science. This book fulfills the needs of engineers, scientists, animators, inventors and others for up-to-date working knowledge of the kinematics of solid bodies presented in an understandable universal format.

Using a synergistic balance of intuition and mathematical logic, the theory of rigid body angular displacement is developed in terms of a rotation vector with very useful geometric properties. Then, this book presents the definitive treatment of rigid body kinematics. This includes formulas on successive rotations, relative rotational motion, general motion of a rigid body, and the motion of systems of coupled bodies (multi-bodies).

The companion volume Production of Motion: Understanding the Dynamics of Rigid Bodies (to be released soon) presents the kinetics of rigid bodies with many useful case studies. DASET Publishing plans to release additional books in the engineering science series.

Cornel J. Rigby enjoyed over 15 years teaching engineering, physics, and CAD courses at institutions abroad and in the U.S.A. He published the book A First Course in Rigid Body Dynamics (1993) and presented or published papers at the Symposium and Workshop of the University of Malawi, the University of Maryland, the Department of Mechanical Engineering Graduate Seminar at Howard University, the American Journal of Physics and other venues.

Cornel enjoyed a fulfilling practice as an engineer in the aerospace industry totaling 12 years with Johns Hopkins University/Applied Physics Laboratory, Martin Marietta Aerospace (now Lockheed-Martin) and McDonnell-Douglas Technical Services Company. He published or presented papers at the JANNAF Propulsion Meeting at Anaheim , the AIAA/AAS Astrodynamics Conference at Palo Alto, the Joint Galileo Flight Design/Flight Operations Working Group Meeting at Houston, and other conferences and symposiums.

In addition, Cornel manages his private practice which he started nearly 20 years ago overseas. He is now full time developing and conducting short courses, writing, publishing, consulting and conducting research. He plans to publish Production of Motion: Understanding the Dynamics of Rigid Bodies Volume II soon and write additional books in the Engineering Science Series. Cornel is a member of PMA and ASME.