Syllabus
* Rotation of coordinate system
Rotation about z-axis, transformation of the Cartesian coordinates under rotation, rotation matrix, description of rotation in terms of the Euler angles and/or in terms of rotation axis and rotation angle, relations between different representations, transformation of Cartesian vectors and tensors under rotation, addition of rotations.
* Rotation of a rigid Earth. Basic aspects
Kinematics of rotation, angular velocity, angular momentum, inertia tensor, principal axes of inertia, kinetic energy, equations of motion for rotation, Euler s equations, free rotation of a rigid Earth, Euler period, free polar motion for a rigid Earth, Chandler period, eigenvalues: axial spin mode and Chandler wobble, solution of inhomogeneous Euler's equations.
* Lunisolar tidal potential
Spherical harmonic representation, zonal tesseral and sectorial parts, representation as a function of time, principal tidal waves, lunisolar torque, particularly for a rotationally symmetric Earth.
* Eigenvalue approach to nutation and polar motion
Body frame, inertial frame, nutation frame, tilt-over mode, prograde motion, retrograde motion, rotation axis figure axis, angular momentum axis, relation between infinitesimal rotation and lunisolar torque, resonance, application to nutation and polar motion, body cone and space cone for free nutation.
* Literature:
- W.H. Munk, G.F. MacDonald, The Rotation of the Earth, Cambridge University Press, New York 1960.
- H. Moritz, I. Mueller, Earth Rotation, Ungarn Publ. Comp., New York 1987.
Annotation
Rotation of coordinate systems, Euler's angles. Lunisolar tidal potential, tidal waves.
Precession and nutation of the rigid Earth, Euler period, Woolard's theory.