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
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