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Extremum principles

Mauro Fabrizio and Morro Angelo

in Electromagnetism of Continuous Media: Mathematical Modelling and Applications

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198527008
eISBN:
9780191713316
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527008.003.0009
Subject:
Mathematics, Applied Mathematics

This chapter shows various ways in which variational formulations can be established. Particular attention is given to the inverse problem, namely, to the determination of a variational formulation, ... More


Lagrangian and Hamiltonian mechanics

D. Violeau

in Fluid Mechanics and the SPH Method: Theory and Applications

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199655526
eISBN:
9780191741227
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655526.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter details the basics of Lagrangian and Hamiltonian mechanics. From the basic principles of mechanics (Galilean invariance, least action principle), the chapter builds the fundamental ... More


The Principle of Least Action: From Teleology to Causality

Yemima Ben-Menahem

in Causation in Science

Published in print:
2018
Published Online:
January 2019
ISBN:
9780691174938
eISBN:
9781400889297
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174938.003.0006
Subject:
History, History of Science, Technology, and Medicine

This chapter examines the place of the “least action” principle in the causal family and its role in in modern science's transition from teleology to causality. It first provides an overview of the ... More


Mathematicians on the geometrization of the Hamilton–Jacobi formalism

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/9780198567370.003.0024
Subject:
Physics, History of Physics

It has long since been remarked by mathematicians that William Rowan Hamilton's method contains purely geometrical truths, and that a peculiar mode of expression, suitable to it, is required in order ... More


From Mechanical Reduction To General Principles

Olivier Darrigol

in Physics and Necessity: Rationalist Pursuits from the Cartesian Past to the Quantum Present

Published in print:
2014
Published Online:
June 2014
ISBN:
9780198712886
eISBN:
9780191781360
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198712886.003.0003
Subject:
Physics, History of Physics

This chapter is devoted to a few general principles that have received mechanical or dynamical justifications: the principle of energy conservation, the principle of least action, and the two laws of ... More


A Hundred and One Years of Mechanics: Newton to Lagrange via Daniel Bernoulli

Jennifer Coopersmith

in Energy, the Subtle Concept: The discovery of Feynman's blocks from Leibniz to Einstein

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198716747
eISBN:
9780191800955
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198716747.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Vis viva (kinetic energy) was discovered by Leibniz, and ‘s Gravesande’s experiments showed that both momentum and kinetic energy were important measures. The concept of ‘potential energy’ slowly ... More


Lagrangian 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/9780198786399.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter shows how the Newtonian law of motion of a particle subject to a gradient force derived from a ‘potential energy’ can always be obtained from an extremal principle, or ‘principle of ... More


Energy, the Subtle Concept: The discovery of Feynman's blocks from Leibniz to Einstein

Jennifer Coopersmith

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198716747
eISBN:
9780191800955
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198716747.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Energy is explained through its history. Newton missed ‘energy’, Leibniz defined kinetic energy, and potential energy emerged from ideas about stored ‘live force’, the concept of ‘work’, analyses of ... More


Beyond the Dynamical Universe: Unifying Block Universe Physics and Time as Experienced

Michael Silberstein, W.M. Stuckey, and Timothy McDevitt

Published in print:
2018
Published Online:
March 2018
ISBN:
9780198807087
eISBN:
9780191844850
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198807087.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics, History of Physics

Theoretical physics and foundations of physics have not made much progress in the last few decades. There is no consensus among researchers on how to approach unifying general relativity and quantum ... More


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