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Rotation of the Earth - NGEO030

Title:	Rotace Země
Guaranteed by:	Department of Geophysics (32-KG)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2018
Semester:	winter
E-Credits:	4
Hours per week, examination:	winter s.:3/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Zdeněk Martinec, DrSc.
Classification:	Physics > Geophysics

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: prof. RNDr. František Gallovič, Ph.D. (21.09.2023)

Rotation of coordinate systems, Euler's angles. Lunisolar tidal potential, tidal waves. Precession and nutation of the rigid Earth, Euler period, Woolard's theory.

Aim of the course -

Last update: prof. RNDr. František Gallovič, Ph.D. (21.09.2023)

The lecture helps students understand general principles of rigid body rotation and their application to Earth rotation.

Literature - Czech

Last update: prof. RNDr. František Gallovič, Ph.D. (21.09.2023)

M. Burša, K. Pěč, Tíhové pole a dynamika Země, Academia, Praha 1988.

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.

Teaching methods -

Last update: T_KG (11.04.2008)

Lecture

Syllabus -

Last update: prof. RNDr. František Gallovič, Ph.D. (21.09.2023)

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.