刚体动力学

本书从现代的观点给出了刚体动力学的系统和完整的介绍，包括李代数、泊松结构、混沌理论和稳定理论。本书描述了位于位势场、流体（基尔霍夫方程）和充满流体的空腔中的刚体运动的主要方程形式。本书所描述的系统都可以用哈密顿函数描述，涉及几乎所有可积情况和目前所知的显式积分方法，对各种刚体动力学中的非可积情况和混沌现象也进行了分析。本书广泛地利用了计算机方法对运动模式进行描述，结合丰富的表格等直观的叙述方式使得读者更易理解本书的内容。
本书适合力学、数学和物理学专业的本科生和研究生，也可供数学物理和动力系统领域的专家参考。

Introduction
The Creators of Rigid Body Dynamics
1 Rigid Body Equations of Motion and Their Integration
1.1 Poisson Brackets and Hamiltonian Formalism
1 Poisson manifolds
Poisson brackets and their properties (19). Nondegenerate brackets,
Symplectic structures (22). Symplectic foliations. Generalized Darboux theorem (22)
2 The Lie-Poisson bracket
1.2 PoincarE and PoincarE-Chetaev Equations
1 PoincarE Equations
2 PoincarE-Chetaev equations
3 Equations on Lie groups
4 Comments
1.3 Various Systems of Variables in Rigid Body Dynamics
1 Euler angles
2 Euler variables. Components of momentum and the direction cosines
3 Quaternion Rodrigues-Hamilton parameters
4 Andoyer variables
5 Comments
1.4 Different Forms of Equations of Motion
1 Equations of motion of a rigid body with a fixed point
Euler-PoincarE equations in the group SO(3) (39). Equations of motion in angular velocities and quaternions (41). Kinetic energy of a rigid body with a fixed point (41).
2 Hamiltonian form of equations of motion for different systems of variables
Equations of motion in algebraic form (42). Quaternion representation of the equations of motion (44). Canonical equations in Euler angles and Andoyer variables (44).
3 PoincarE section and chaotic motions
1.5 Equations of Motion of a Rigid Body in Euclidean Space
1 Lagrangian formalism and Poincare equations on the group E(3)
2 Kinetic energy of a rigid body in R3
3 Hamiltonian form of equations of motion of a rigid body in R3
1.6 Examples and Similar Problems
1 Motion of a rigid body with a fixed point in a superposition of constant uniform force fields
2 A free rigid body in a quadratic potential
3 Motion of a rigid body with a fixed point in a rotating coordinate system
Gyroscope and Foucault pendulum (56). A satellite on a circular earth orbit (56).
4 Relative motion of a rigid body with a fixed point
5 Motion of a rigid body sliding on a smooth plane
6 Gyroscope in the Cardan suspension
7 Motion of a rigid body in an ideal incompressible fluid and the Kirchhoff equations
8 Falling rigid body in an ideal fluid
9 The Levitron
1.7 Theorems on Integrability and Methods of Integration
1 Hamiltonian systems. The Liouville-Arnold theorem
2 Theory of the last multiplier. Euler-Jacobi theorem
3 Separation of variables. Hamilton-Jacobi method
Geodesic flow on the ellipsoid (Jacobi problem) (73). System with
quadratic potential on a sphere (Neumann problem) (74).
2 The Euler-Poisson Equations and Their Generalizations
3 The Kirchhoff Equations and Related Problems of Rigid Body Dynamics