Syllabus
* Rotation of coordinate systems
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 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, nutation, precession.
* Coordinate systems on a deforming Earth
Wilson cycle, Plate motion reconstruction from marine data, Apparent polar wander paths of continents, Euler pole, Paleopoles, Hot-spot reference frame, Tisserand axes
* Conservation laws in a rotating frame
Extension of continuum mechanics fundamental balance laws into non-inertial frames of reference, Fictitious forces: Euler, Centrifugal, Coriolis force
* Motion of the Earth's rotation pole
Liouville equation, planetary reorientation, polar motion on tidally locked bodies, core-mantle coupling
Annotation
Rigid body rotation, Euler's angles. Precession and nutation of the rigid Earth, Euler period.
Frames of reference on a deforming body. Polar wander, Planetary reorientation.