Gyrodampers for large space structures

The problem of controlling the vibrations of a large space structures by the use of actively augmented damping devices distributed throughout the structure is addressed. The gyrodamper which consists of a set of single gimbal control moment gyros which are actively controlled to extract the structural vibratory energy through the local rotational deformations of the structure, is described and analyzed. Various linear and nonlinear dynamic simulations of gyrodamped beams are shown, including results on self-induced vibrations due to sensor noise and rotor imbalance. The complete nonlinear dynamic equations are included. The problem of designing and sizing a system of gyrodampers for a given structure, or extrapolating results for one gyrodamped structure to another is solved in terms of scaling laws. Novel scaling laws for gyro systems are derived, based upon fundamental physical principles, and various examples are given

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Glosarium Matematika

273 p.; 24 cm

The Hardy-Ramanujan-Rademacher expansion for the partition function and its extensions

Partition theory has been studied more extensively during the last century, athough it has been around since Euler. It is not only because its combinatorial or classical analytical aspects, but also because of the opportunities number theorists saw in applications of modular forms in a di erent and deep view. In this thesis, we study exact formulas for the number of various partitions. For each one, we need to prove a modular transformation formula, and use Farey dissection to avoid the essential singularities of the generating functions. After that, we need to control or estimate the resulting integrals which are rooted from Cauchy integral formula. In this way, we rst study an exact formula for the number of ordinary partitions of any given integer. This formula is a famous result by Ramanujan, Hardy, and Rademacher. Also, we studied another well-known result by Hao, which gives an exact formula for the number of partitions into odd parts. This partition can also be considered for the partitions with distinct parts, thanks to Euler's partition identity. The generating function is a modular form which needs Kloosterman's estimates to handle the integrals. Next, we propose a result which is aimed at the colored partitions with parts of the form 10t±a or 2t±1. This is a continuation of recent works to generalize to partitions into parts in certain symmetric residue classes modulo a given integer. Finally, we will explain about possible future plans to nd exact formulas for various other partition functions

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Research in computerized structural analysis and synthesis

Computer applications in dynamic structural analysis and structural design modeling are discussed