Geomathematically Oriented Potential Theory [Hardcover]

As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and todays satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earths gravitational and magnetic field.

Geomathematically Oriented Potential Theorypresents the principles of space and surface potential theory involving Euclidean and spherical concepts. The authors offer new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework.

The book begins with notational material and the necessary mathematical background. The authors then build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They also discuss surface potential theory on the unit sphere along with corresponding applications.

Focusing on the state of the art, this book breaks new geomathematical grounds in gravitation and geomagnetism. It explores modern sphere-oriented potential theoretic methods as well as classical space potential theory.

PRELIMINARIES
Three-Dimensional Euclidean Space R³
Basic Notation
Integral Theorems

Two-Dimensional Sphere ?
Basic Notation
Integral Theorems
(Scalar) Spherical Harmonics
(Scalar) Circular Harmonics
Vector Spherical Harmonics
Tensor Spherical Harmonics

POTENTIAL THEORY IN THE EUCLIDEAN SPACE R³
Basic Concepts
Background Material
Volume Potentials
Surface Potentiallã2