978 - 0 - 521 - 11309 - 0 - Ellipsoidal Harmonics : Theory and Applications
نویسنده
چکیده
The sphere, because of its high symmetry, is what might be called a perfect shape. Unfortunately nature is imperfect and many apparently spherical bodies are better represented by an ellipsoid. Consequently in calculations about gravitational potential, for example, spherical harmonics have to be replaced by the much more complex ellipsoidal harmonics. Their theory, which was originated in the nineteenth century, could only be seriously applied with the kind of computational power that has become available in recent years. This, therefore, is the first book completely devoted to ellipsoidal harmonics. After a complete presentation of the theory, applied topics are drawn from geometry, physics, biosciences, and inverse problems. The book contains classical results as well as new material, including ellipsoidal biharmonic functions, the theory of images in ellipsoidal geometry, geometrical characteristics of surface perturbations, and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader’s understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers, and for anyone who needs to know the current state of the art in this fascinating subject. Specific chapters can serve as teaching material.
منابع مشابه
Using Ellipsoidal Harmonics for 3D Shape Representation and Retrieval
A novel approach for 3D Shape description, applicable for search and retrieval applications, based on the theory of Ellipsoidal Harmonics is presented in this paper. The Ellipsoidal Harmonics are appropriately adopted in order to describe volumetric represented 3D objects. The experimental results, performed in a complete 3D object database, prove the efficiency of the proposed approach.
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