## Observer-independent Dynamical Measures of Team Coordination and Performance

*Silke M. Dodel, Ajay S. Pillai, Philip W. Fink, Eric R. Muth, Roy Stripling, Dylan D. Schmorrow, Joseph V. Cohn, and Viktor K. Jirsa*

### in Motor Control: Theories, Experiments, and Applications

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780195395273
- eISBN:
- 9780199863518
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195395273.003.0004
- Subject:
- Neuroscience, Sensory and Motor Systems

Team performance represents an extension of individual performance. It is an outcome of individuals joining together for the purpose of exploiting one another's individual skills to accomplish ... More

## A Primer for Dynamical Systems

*Kevin S. McCann*

### in Food Webs (MPB-50)

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691134178
- eISBN:
- 9781400840687
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691134178.003.0002
- Subject:
- Biology, Ecology

This chapter introduces the reader to some of the main conceptual ideas behind dynamical systems theory from the perspective of an experimentalist. It first considers the qualitative approaches used ... More

## Hamilton’s Principle

*Oliver Johns*

### in Analytical Mechanics for Relativity and Quantum Mechanics

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.003.0006
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The general calculus of variations discussed in the previous chapter may be used to derive variational principles in mechanics. Two different, but closely related, variational principles are ... More

## Collective descriptions of beam distributions

*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/9780198525547.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter generalizes the description of charged particle motion from a single particle viewpoint to one concerned with distributions in phase space. It discusses that the first classes of ... More

## OUTLOOK

*Francesco Calogero*

### in Isochronous Systems

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199535286
- eISBN:
- 9780191715853
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199535286.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In Chapter 8 five directions of future research are tersely mentioned in order of increasing importance. The investigation of Diophantine relations, such as those reported in Appendix C. The ... More

## Coherent states

*J. C. Garrison and R. Y. Chiao*

### in Quantum Optics

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198508861
- eISBN:
- 9780191708640
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508861.003.0006
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The elementary quantum theory of quasi-classical states for mechanical harmonic oscillators is applied to the radiation oscillators describing light, and thus used to define quasi-classical states of ... More

## Bose–Hubbard models: methods of treatment

*Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger*

### in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199573127
- eISBN:
- 9780191775048
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573127.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter reviews various theoretical methods that can be applied to investigate Bose–Hubbard models. In particular, it discusses the Bogolyubov method, strong coupling expansion, the perturbative ... More

## Hamiltonian Mechanics with Time as a Coordinate

*Oliver Johns*

### in Analytical Mechanics for Relativity and Quantum Mechanics

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.003.0012
- Subject:
- Physics, Atomic, Laser, and Optical Physics

In the previous chapter, the traditional Lagrange equations were used as the basis for an extended Lagrangian theory in which time is treated as a coordinate. This extended theory combined the ... More

## Particle Motion in Curved Spacetime

*Valeri P. Frolov and Andrei Zelnikov*

### in Introduction to Black Hole Physics

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199692293
- eISBN:
- 9780191731860
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199692293.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Particle motion in a curved spacetime is considered. The Lagrangian and Hamiltonian form of the equation of motion of a relativistic particle are described. We discuss here also the Hamilton‐Jacobi ... More

## Linear transverse motion

*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/9780198525547.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter begins with a discussion that deepened the introductory remarks made on betatron oscillations. It explains that in such a scheme, one can have simultaneous stability in both vertical and ... More

## Introduction To Hamiltonian Mechanics

*Oliver Johns*

### in Analytical Mechanics for Relativity and Quantum Mechanics

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.003.0004
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The power of Lagrangian mechanics has caused generations of students to wonder why it is necessary or even desirable, to recast mechanics in Hamiltonian form. The answer is that the Hamiltonian ... More

## Path Integrals In Quantum Mechanics: Generalizations

*JEAN ZINN-JUSTIN*

### in Quantum Field Theory and Critical Phenomena

- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780198509233
- eISBN:
- 9780191708732
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509233.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 2 constructed a path integral representation of the matrix elements of the statistical operator e-βH. This chapter extends the construction to hamiltonians which are general functions of ... More

## PATH INTEGRALS IN PHASE SPACE

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter contains a few additional results such as a definition of path integrals over phase space trajectories, and the problems generated by the quantization of lagrangians with potentials ... More

## Canonical Transformations

*Oliver Johns*

### in Analytical Mechanics for Relativity and Quantum Mechanics

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.003.0017
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter considers a broader class of transformations known as canonical transformations, which transform the whole of the extended phase space in a more general way. Each new canonical ... More

## ISOCHRONOUS SYSTEMS ARE NOT RARE

*Francesco Calogero*

### in Isochronous Systems

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199535286
- eISBN:
- 9780191715853
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199535286.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In Chapter 2 a simple trick—amounting to a change of variables—is introduced that modifies a large class of dynamical systems so that the (autonomous) ω-modified systems thereby obtained are ... More

## Circulating beams

*E. J. N. Wilson*

### in An Introduction to Particle Accelerators

- Published in print:
- 2001
- Published Online:
- January 2010
- ISBN:
- 9780198508298
- eISBN:
- 9780191706363
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508298.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter opens with a discussion of Liouville's theorem—a conservation principle that applies to the area of phase space, usually an ellipse, occupied by a beam. In the transverse phase plane, ... More

## Bayesian reconstruction of particle beam phase space

*C Nakhleh, D Higdon, C K Allen, and R Ryne*

### in Bayesian Theory and Applications

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199695607
- eISBN:
- 9780191744167
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695607.003.0033
- Subject:
- Mathematics, Probability / Statistics

This chapter discusses the application of Bayesian inversion methodology to reconstruct the initial phase space configuration of charged particle beams using a series of one-dimensional projection ... More

## Kinetically constrained models

*Juan P. Garrahan, Peter Sollich, and Cristina Toninelli*

### in Dynamical Heterogeneities in Glasses, Colloids, and Granular Media

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199691470
- eISBN:
- 9780191729799
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691470.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter summarizes recent developments in the study of kinetically constrained models (KCMs) as models for glass formers. After recalling the definition of the KCMs which are covered in this ... More

## Hamilton’s Principle and Noether’s Theorem

*Oliver Johns*

### in Analytical Mechanics for Relativity and Quantum Mechanics

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.003.0013
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses ... More

## Phase Space Reconstruction

*Ray Huffaker, Marco Bittelli, and Rodolfo Rosa*

### in Nonlinear Time Series Analysis with R

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198782933
- eISBN:
- 9780191826153
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198782933.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical ... More