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## Introduction to beam physics

*J. B. Rosenzweig*

### in Fundamentals of Beam Physics

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198525547
- eISBN:
- 9780191711725
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525547.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter begins by introducing particle accelerators in their scientific and historical context. It reviews methods in Lagrangian and Hamiltonian dynamics as well as special relativity in a ... More

## Fundamentals of Beam Physics

*J. B. Rosenzweig*

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198525547
- eISBN:
- 9780191711725
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525547.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This book presents beam physics using a unified approach, emphasizing basic concepts and analysis methods. While many existing resources in beams and accelerators are specialized to aid the ... More

## Tonelli Lagrangians and Hamiltonians on Compact Manifolds

*Alfonso Sorrentino*

### in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164502
- eISBN:
- 9781400866618
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164502.003.0001
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces the basic setting: Tonelli Lagrangians and Hamiltonians on a compact manifold. It discusses their main properties and some examples, and provides the opportunity to recall ... More

## Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

*Alfonso Sorrentino*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164502
- eISBN:
- 9781400866618
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164502.001.0001
- Subject:
- Mathematics, Applied Mathematics

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical ... More

## Charged particle motion in static fields

*J. B. Rosenzweig*

### in Fundamentals of Beam Physics

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198525547
- eISBN:
- 9780191711725
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525547.003.0002
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter is concerned with introducing a number of model problems, based on the relativistic motion of charged particles in static electric and magnetic field configurations. It discusses that ... More

## Hamiltonian Formulation

*Flavio Mercati*

### in Shape Dynamics: Relativity and Relationalism

- Published in print:
- 2018
- Published Online:
- April 2018
- ISBN:
- 9780198789475
- eISBN:
- 9780191831294
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198789475.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

The Hamiltonian formulation of relational particle dynamics unveils its equivalence with modern gauge theory, which admits exactly the same canonical formulation. Both are constrained Hamiltonian ... More

## Wave Turbulence

*Vladimir Zeitlin*

### in Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

- Published in print:
- 2018
- Published Online:
- April 2018
- ISBN:
- 9780198804338
- eISBN:
- 9780191842627
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198804338.003.0013
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

Main notions and ideas of wave (weak) turbulence theory are explained with the help of Hamiltonian approach to wave dynamics, and are applied to waves in RSW model. Derivation of kinetic equations ... More

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