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Integral principles

JESPER LÜTZEN

in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567370
eISBN:
9780191717925
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567370.003.0021
Subject:
Physics, History of Physics

In his book Principles of Mechanics, Heinrich Hertz treats integral principles in three parts. First, he discusses the properties of geodesics and their relation to straightest paths in a purely ... More


The View from General Relativity

Harvey R. Brown

in Physical Relativity: Space-time structure from a dynamical perspective

Published in print:
2005
Published Online:
September 2006
ISBN:
9780199275830
eISBN:
9780191603914
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199275831.003.0009
Subject:
Philosophy, Philosophy of Science

In his 1923 book The Mathematical Theory of Relativity, Arthur Eddington distinguished between two chains of reasoning in general relativity. The first familiar one starts with the existence of the ... More


RADON TRANSFORM ON GROUPS

Leon Ehrenpreis

in The Universality of the Radon Transform

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198509783
eISBN:
9780191709166
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509783.003.0007
Subject:
Mathematics, Mathematical Physics

This chapter applies the book's methods to various Lie groups. In particular, to the horocyclic and geodesic transforms on G/K.


Lorentz Geometry

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0001
Subject:
Mathematics, Applied Mathematics

This chapter presents a survey of the basic definitions of Riemannian and Lorentzian differential geometry used in this book. The first nine sections use the simplest formulations, in local ... More


Hyperbolic Dynamics and Brownian Motion: An Introduction

Jacques Franchi and Yves Le Jan

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199654109
eISBN:
9780191745676
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199654109.001.0001
Subject:
Mathematics, Mathematical Physics

The idea of this book is to illustrate an interplay between distinct domains of mathematics. Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group PSO(1, d) ... More


The Built Environment: Buckminster Fuller's Spaceship Earth

Linda Sargent Wood

in A More Perfect Union: Holistic Worldviews and the Transformation of American Culture after World War II

Published in print:
2010
Published Online:
September 2010
ISBN:
9780195377743
eISBN:
9780199869404
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195377743.003.0003
Subject:
History, American History: 20th Century

Structural engineer Buckminster Fuller's geodesic dome was a visible manifestation of holism. Held together in what he described as “synergetic” wholeness, each part relying on neighboring parts for ... More


On Relativity, Time Reckoning, and the Topology of Time Series

Roberto Torretti

in The Arguments of Time

Published in print:
2006
Published Online:
January 2012
ISBN:
9780197263464
eISBN:
9780191734748
Item type:
chapter
Publisher:
British Academy
DOI:
10.5871/bacad/9780197263464.003.0004
Subject:
Philosophy, General

This chapter devotes equal attention to special relativity and general relativity. It first describes the history of the analysis of distant simultaneity, up to and including Einstein's procedure in ... More


The geometric approach to GWs

Michele Maggiore

in Gravitational Waves: Volume 1: Theory and Experiments

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570745
eISBN:
9780191717666
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570745.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations ... More


Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

S. G. Rajeev

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the ... More


Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Christopher D. Sogge

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160757
eISBN:
9781400850549
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160757.001.0001
Subject:
Mathematics, Numerical Analysis

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. The book gives a proof of the sharp Weyl ... More


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