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Formulations of the Einstein–Euler Equations

Luciano Rezzolla and Olindo Zanotti

in Relativistic Hydrodynamics

Published in print:
2013
Published Online:
January 2014
ISBN:
9780198528906
eISBN:
9780191746505
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528906.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter, which opens the second part of the book devoted to the numerical solution of the relativistic-hydrodynamics equations, presents in a concise, yet complete, way the several formulations ... More


Mathematics supplements

Ta-Pei Cheng

in Einstein's Physics: Atoms, Quanta, and Relativity - Derived, Explained, and Appraised

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199669912
eISBN:
9780191744488
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199669912.003.0018
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Differential and integral vector calculus is reviewed so that a reader can understand the connection between Maxwell’s equations written as integral relations and as differential equations (as ... More


Absolute time

George Jaroszkiewicz

in Images of Time: Mind, Science, Reality

Published in print:
2016
Published Online:
January 2016
ISBN:
9780198718062
eISBN:
9780191787553
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198718062.003.0014
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses Newton’s concept of absolute time and its use in classical mechanics. It defines clocks and our freedom to change them, that is, reparametrization of time. The chapter goes on ... More


Antecedents

Jennifer Coopersmith

in The Lazy Universe: An Introduction to the Principle of Least Action

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198743040
eISBN:
9780191802966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198743040.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Early ideas about optimization principles were brought in by an eclectic group of extraordinary thinkers: the Ancients (Hero, and Princess Dido), Fermat with his Principle of Least Time, the ... More


Mathematics and physics preliminaries: of hills and plains and other things

Jennifer Coopersmith

in The Lazy Universe: An Introduction to the Principle of Least Action

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198743040
eISBN:
9780191802966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198743040.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

The link between mathematics and physics is explained, and how the concepts “coordinates,” “generalized coordinates,” “time,” and “space” have evolved, starting with Galileo. It is also shown that ... More


Introduction

Laurent Baulieu, John Iliopoulos, and Roland Sénéor

in From Classical to Quantum Fields

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198788393
eISBN:
9780191830310
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198788393.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is ... More


Dynamics of massive systems

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents the laws of motion of an ensemble of point masses forming a solid body whose shape is invariant, or a fluid whose shape can vary with time. It argues that an ensemble of point ... More


Hamiltonian mechanics

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0009
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter gives a brief overview of Hamiltonian mechanics. The complexity of the Newtonian equations of motion for N interacting bodies led to the development in the late 18th and early 19th ... More


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