Fox, Henrici, and Moler made famous a “Method of Particular Solutions” for computing eigenvalues and eigenmodes of the Laplacian in planar regions such as polygons. We explain why their formulation of this method breaks down when applied to regions that are insufficiently simple and propose a modification that avoids these difficulties. The crucial changes are to introduce points in the interio...

1 Major Errata 1. A serious typographical error was made in the proofs with respect to the vector curvature symbol: κ. The scalar (summed) curvature should be denoted by κ; the vector (summed) curvature should be denoted by κ := κν, where ν is the normal vector of the surface. Unfortunately, the bold was omitted in several places in the final version of the book, especially Ch. 6 and Ch. 7. In ...

Satellite Laser Ranging (SLR) systems successfully measure attitude and spin period of Envisat. During the International Laser Ranging Service (ILRS) campaign the SLR stations observed the satellite and provided measurements that allow determination of the attitude and the spin period of Envisat during year 2013. The spin parameters of the spacecraft are stable within a coordinate system fixed ...

In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel theoretical result of this work is that, for a ring structure with m subunits, the symmetricity of the normal modes falls into m groups of equal size, with norm...