Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.
This self-contained textbook with exercises discusses a broad range of selected topics from classical mechanics and electromagnetic theory that inform key issues related to modern accelerators. Part I presents fundamentals of the Lagrangian and Hamiltonian formalism for mechanical systems, canonical transformations, action-angle variables, and then linear and nonlinear oscillators. The Hamiltonian for a circular accelerator is used to evaluate the equations of motion, the action, and betatron oscillations in an accelerator. From this base, we explore the impact of field errors and nonlinear resonances. This part ends with the concept of the distribution function and an introduction to the kinetic equation to describe large ensembles of charged particles and to supplement the previous single-particle analysis of beam dynamics. Part II focuses on classical electromagnetism and begins with an analysis of the electromagnetic field from relativistic beams, both in vacuum and in a resistive pipe. Plane electromagnetic waves and modes in waveguides and radio-frequency cavities are also discussed. The focus then turns to radiation processes of relativistic beams in different conditions, including transition, diffraction, synchrotron, and undulator radiation. Fundamental concepts such as the retarded time for the observed field from a charged particle, coherent and incoherent radiation, and the formation length of radiation are introduced. We conclude with a discussion of laser-driven acceleration of charged particles and the radiation damping effect. Appendices on electromagnetism and special relativity are included, and references are given in some chapters as a launching point for further reading. This text is intended for graduate students who are beginning to explore the field of accelerator physics, but is also recommended for those who are familiar with particle accelerators but wish to delve further into the theory underlying some of the more pressing concerns in their design and operation.
This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up-to-date, comprehensive, designed for teaching, and is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. Part II is concerned with different approaches for modelling or simulating turbulent flows. The necessary mathematical techniques are presented in the appendices. This book is primarily intended as a graduate level text in turbulent flows for engineering students, but it may also be valuable to students in applied mathematics, physics, oceanography and atmospheric sciences, as well as researchers and practising engineers. Contents Preface; Nomenclature; Part I. Fundamentals: 1. Introduction; 2. The equations of flu
In a nutshell, it´s an eleven string, fretless, acoustic/electric instrument, strung with nylon strings and tuned to standard guitar tuning. More than ever before, musicians are mixing sounds and musical styles from all over the world. This often involves the mixing of Eastern and Western music, such as using a Sitar in a western musical setting or using western instruments to imitate the sounds in eastern music. The Glissentar was inspired by a similar desire to mix elements of East and West, but in this case, in the instrument itself. The Western part of the equation is easy to recognize as a variation on the guitar. All of the instruments basic dimensions, scale length, body size, depth, fingerboard radius, and string height, are fairly standard for acoustic/electric guitars. The Eastern influence in the Glissentar comes from the Oud, an ancestor of the Mandolin that dates back to the seventh century. The Oud is also an eleven-string fretless instrument and is still in use today primarily in Armenia and Egypt. Adapting to this new instrument is actually a great deal easier than it appears. The shape and scale of the neck and the easily visible side position markers help to give the Glissentar a very familiar feel. The Glissentar opens the door to microtonal playing as well as some incredible and unique new sounds for adventurous guitar players.SpecsRock Maple neckEbony Fingerboard16 fingerboard radius25 1/2 Scale1 3/4 nut widthTwo-Chamber Silver Leaf Maple bodySolid Cedar TopGodin Custom under-saddle Transducer & custom preampVolume, Mid, Treble and Bass controls