●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

本書從現代的觀點給出了剛體動力學的繫統和完整的介紹，包括李代數、泊松結構、混沌理論和穩定理論。本書描述了位於位勢場、流體（基爾霍夫方程）和充滿流體的空腔中的剛體運動的主要方程形式。本書所描述的繫統都可以用哈密頓函數描述，涉及幾乎所有可積情況和目前所知的顯式積分方法，對各種剛體動力學中的非可積情況和混沌現像也進行了分析。本書廣泛地利用了計算機方法對運動模式進行描述，結合豐富的表格等直觀的敘述方式使得讀者更易理解本書的內容。
本書適合力學、數學和物理學專業的本科生和研究生，也可供數學物理和動力繫統領域的專家參考。