Rotational Motion of Celestial Bodies

This book presents a basic theoretical treatment of rotational motion that is applicable to the Earth, Moon, solid planets, satellites, asteroids, and other rigid-body-like celestial bodies. Starting from the concept of rigid bodies, the book describes necessary mathematical tools such as rotation matrices or Euler angles. The book is structured to derive the basic equation of motion by regarding the finite body as a group of particles under constraint. The solution of the body's free motion is elucidated completely using the elliptic functions and incomplete elliptic integrals. Their numerical computation is briefly explained in the Appendix. In addition, the book discusses the approximated solution of rotation under gravitational tidal torque. This process leads to a rough estimate of the forced precession, nutation, and length-of-day variation of the Earth and other bodies. Appropriate for the advanced level of the material, two types of treatments of analytical dynamics are described: those of Lagrange and Hamilton. Finally, the book presents applications including the rotation of Ceres. The general level of the book is suitable for those in graduate courses of study.