 Rigid Body Mechanics: Mathematics, Physics and Applications
ISBN: 978-3-527-40620-3
Paperback
262 pages
January 2006
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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.
