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Rotation of the Earth - NGEO030

Title:	Rotace Země
Form of teaching:	lecture
Guaranteed by:	Department of Geophysics (32-KG)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2026
Duration in semesters:	1
Semester:	winter
E-Credits:	4
Hours per week, examination:	winter s.:3/0, Ex [HT]
Capacity:	unlimited
Maximum number of enrolled students:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Repeated enrollment:	2 / 2 / 2 / 2

Guarantor:	RNDr. Vojtěch Patočka, Ph.D.
Teacher(s):	RNDr. Vojtěch Patočka, Ph.D.
Classification:	Physics > Geophysics

Opinion survey results WS schedule Noticeboard

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.

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

Aim of the course -

The lecture helps students understand general principles of rigid body rotation and their application to planetary bodies that not only rotate, but are also subject to tides and internal deformation.

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

Course completion requirements -

Oral exam

Last update: Gallovič František, prof. RNDr., Ph.D. (10.06.2019)

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.

Langer J., Podolský, J., Kinematika tuhého tělesa - lecture notes

Matsuyama, I., Nimmo, F., Mitrovica, J.X., 2014. Planetary reorientation. Annu. Rev. Earth Planet. Sci. 42, 605-634.

Trond H. Torsvik, R. Dietmar Müller, Rob Van der Voo, Bernhard Steinberger, and Carmen Gaina: Global plate motion frames: toward a unified model

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

Teaching methods -

Lecture

Last update: T_KG (11.04.2008)

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

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