Rigid Body Dynamics

Introduction.- Part 1. Overview of Rigid Body Dynamics.- Distribution of mass.- Description of rotation of a rigid body about a fixed point.- The classical problem: The motion of a heavy rigid body about a fixed point.- General and conditional integrable cases of the classical problem.- The motion of a heavy gyrostat.- Motion of rigid body about a fixed point in the field of a distant Newtonian centre and Brun's problem.- The motion of a body with no fixed point.- Part 2. Research on Rigid Body Dynamics.- Particular solutions of the classical problem and its generalizations.- The rigid body in a potential field.- The problem of motion of a body in a liquid.- The general problem of motion of a rigid body acted upon by a coaxial combination of potential and gyroscopic forces.- The most general integrable in rigid body dynamics.- Miscellaneous cases integrable on a single level of the areas integral.- The rigid body acted upon by a skew combination of fields.