This textbook is a modern, concise and focused treatment of the mathematical techniques, physical theories and applications of rigid body mechanics, bridging the gap between the geometric and more classical approaches to the topic. It emphasizes the fundamentals of the subject, stresses the importance of notation, integrates the modern geometric view of mechanics and offers a wide variety of examples ranging from molecular dynamics to mechanics of robots and planetary rotational dynamics. The author has unified his presentation such that applied mathematicians, mechanical and astro aerodynamical engineers, physicists, computer scientists and astronomers can all meet the subject on common ground, despite their diverse applications.
William B. Heard holds an M.A. in Mathematics from the University of Colorado and a Ph.D. and M.Phil. in Astronomy from Yale University. From 1973 to 1975, he taught as an Assistant Professor of Mathematics at the U.S. Naval Academy and in 1975 accepted a post as Scientist at the Naval Research Laboratory. Here, he developed theoretical and computational techniques for space systems and internal ocean waves. From 1978 to 2003, Dr. Heard worked as a Scientist for Exxon/Exxon Mobil Research and Engineering. During these years, he held a variety of adjunct teaching positions at Rutgers University, Stevens Institute of Technology and Fairleigh Dickinson University where he taught numerical methods, computational fluid dynamics and continuum mechanics. In 2003, Dr. Heard took retirement and now works as an independent writer.
Preface. 1 Rotations. 1.1 Rotations as Linear Operators. 1.2 Quaternions. 1.3 Complex Numbers. 1.4 Summary. 1.5 Exercises. 2 Kinematics, Energy, and Momentum. 2.1 Rigid Body Transformation. 2.2 Angular Velocity. 2.3 The Inertia Tensor. 2.4 Angular Momentum. 2.5 Kinetic Energy. 2.6 Exercises. 3 Dynamics. 3.1 Vectorial Mechanics. 3.2 Lagrangian Mechanics. 3.3 Hamiltonian Mechanics. 3.4 Exercises. 4 Constrained Systems. 4.1 Constraints. 4.2 Lagrange Multipliers. 4.3 Applications. 4.4 Alternatives to Lagrange Multipliers. 4.5 The Fiber Bundle Viewpoint. 4.6 Exercises. 5 Integrable Systems. 5.1 Free Rotation. 5.2 Lagrange Top. 5.3 The Gyrostat. 5.4 Kowalevsky Top. 5.5 Liouville Tori and Lax Equations. 5.6 Exercises. 6 Numerical Methods. 6.1 Classical ODE Integrators. 6.2 Symplectic ODE Integrators. 6.3 Lie Group Methods. 6.4 Differential-Algebraic Systems. 6.5 Wobblestone Case Study. 6.6 Exercises. 7 Applications. 7.1 Precession and Nutation. 7.2 Gravity Gradient Stabilization of Satellites. 7.3 Motion of a Multibody: A Robot Arm. 7.4 Molecular Dynamics. Appendix. A Spherical Trigonometry. B Elliptic Functions. B.1 Elliptic Functions Via the Simple Pendulum. B.2 Algebraic Relations Among Elliptic Functions. B.3 Differential Equations Satisfied by Elliptic Functions. C Lie Groups and Lie Algebras. C.1 Infinitesimal Generators of Rotations. C.2 Lie Groups. C.3 Lie Algebras. C.4 Lie Group-Lie Algebra Relations. D Notation. References. Index.