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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


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


Autonomous Geometrical Mechanics

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0022
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic ... More


The reparametrization of 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/9780198718062.003.0015
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter reviews the parametrization of absolute time and develop the concept of temporal reparametrizations, or changes in our clocks. Using the action integral and Dirac’s constraint mechanics, ... More


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