Rigid Body Mechanics : Mathematics, Physics and Applications
William B. Heard
Bok Engelsk 2008 · Electronic books.
| Utgitt | Hoboken : : Wiley, , 2008.
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| Omfang | 1 online resource (265 p.)
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| Opplysninger | Description based upon print version of record.. - Rigid Body Mechanics; Contents; Preface; 1 Rotations; 1.1 Rotations as Linear Operators; 1.1.1 Vector Algebra; 1.1.2 Rotation Operators on R3; 1.1.3 Rotations Specified by Axis and Angle; 1.1.4 The Cayley Transform; 1.1.5 Reflections; 1.1.6 Euler Angles; 1.2 Quaternions; 1.2.1 Quaternion Algebra; 1.2.2 Quaternions as Scalar-Vector Pairs; 1.2.3 Quaternions as Matrices; 1.2.4 Rotations via Unit Quaternions; 1.2.5 Composition of Rotations; 1.3 Complex Numbers; 1.3.1 Cayley-Klein Parameters; 1.3.2 Rotations and the Complex Plane; 1.4 Summary; 1.5 Exercises; 2 Kinematics, Energy, and Momentum. - 2.1 Rigid Body Transformation2.1.1 A Rigid Body has 6 Degrees of Freedom; 2.1.2 Any Rigid Body Transformation is Composed of Translation and Rotation; 2.1.3 The Rotation is Independent of the Reference Point; 2.1.4 Rigid Body Transformations Form the Group SE(3); 2.1.5 Chasles' Theorem; 2.2 Angular Velocity; 2.2.1 Angular Velocity in Euler Angles; 2.2.2 Angular Velocity in Quaternions; 2.2.3 Angular Velocity in Cayley-Klein Parameters; 2.3 The Inertia Tensor; 2.4 Angular Momentum; 2.5 Kinetic Energy; 2.6 Exercises; 3 Dynamics; 3.1 Vectorial Mechanics; 3.1.1 Translational and Rotational Motion. - 3.1.2 Generalized Euler Equations3.2 Lagrangian Mechanics; 3.2.1 Variational Methods; 3.2.2 Natural Systems and Connections; 3.2.3 Poincaré's Equations; 3.3 Hamiltonian Mechanics; 3.3.1 Momenta Conjugate to Euler Angles; 3.3.2 Andoyer Variables; 3.3.3 Brackets; 3.4 Exercises; 4 Constrained Systems; 4.1 Constraints; 4.2 Lagrange Multipliers; 4.2.1 Using Projections to Eliminate the Multipliers; 4.2.2 Using Reduction to Eliminate the Multipliers; 4.2.3 Using Connections to Eliminate the Multipliers; 4.3 Applications; 4.3.1 Sphere Rolling on a Plane; 4.3.2 Disc Rolling on a Plane. - 4.3.3 Two-Wheeled Robot4.3.4 Free Rotation in Terms of Quaternions; 4.4 Alternatives to Lagrange Multipliers; 4.4.1 D'Alembert's Principle; 4.4.2 Equations of Udwadia and Kalaba; 4.5 The Fiber Bundle Viewpoint; 4.6 Exercises; 5 Integrable Systems; 5.1 Free Rotation; 5.1.1 Integrals of Motion; 5.1.2 Reduction to Quadrature; 5.1.3 Free Rotation in Terms of Andoyer Variables; 5.1.4 Poinsot Construction and Geometric Phase; 5.2 Lagrange Top; 5.2.1 Integrals of Motion and Reduction to Quadrature; 5.2.2 Motion of the Top's Axis; 5.3 The Gyrostat; 5.3.1 Bifurcation of the Phase Portrait. - 5.3.2 Reduction to Quadrature5.4 Kowalevsky Top; 5.5 Liouville Tori and Lax Equations; 5.5.1 Liouville Tori; 5.5.2 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; 7.1.1 Gravitational Attraction; 7.1.2 Precession and Nutation via LagrangianMechanics; 7.1.3 A Hamiltonian Formulation; 7.2 Gravity Gradient Stabilization of Satellites; 7.2.1 Kinematics in Terms of Yaw-Pitch-Roll. - 7.2.2 Rotation Equations for an Asymmetric Satellite. - 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-aerodyna
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| Emner | |
| Sjanger | |
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| ISBN | 3527406204. - 9783527406203
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