Journal ArticleDOI
Generalized Hamiltonian dynamics
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The equations of dynamics were put into a general form by Lagrange, who expressed them in terms of a set of generalized coordinates and velocities as discussed by the authors, and an alternative general form was later given by Hamilton, in the form of coordinates and momenta.Abstract:
1. Introduction. The equations of dynamics were put into a general form
by Lagrange, who expressed them in terms of a set of generalized coordinates
and velocities. An alternative general form was later given by Hamilton, in
terms of coordinates and momenta. Let us consider the relative merits of the
two forms.read more
Citations
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Nonperturbative quantum geometries
TL;DR: Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, this paper presented an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint.
Journal ArticleDOI
Gauge invariance and degree of freedom count
Marc Henneaux,Marc Henneaux,Claudio Teitelboim,Claudio Teitelboim,Claudio Teitelboim,Jorge Zanelli,Jorge Zanelli,Jorge Zanelli +7 more
TL;DR: In this article, the precise relation between the gauge transformations in lagrangian and hamiltonian form is derived for any gauge theory, and the analysis yields as by-products: (i) a systematic way to derive all the gauge symmetries of a given Lagrangian; (ii) a precise criterion for counting the physical degrees of freedom of a gauge theory directly from the form of gauge transformations.
Journal ArticleDOI
Resonant post-newtonian eccentricity excitation in hierarchical three-body systems
TL;DR: In this paper, a post-Newtonian expansion of general relativity (GR) was studied for the hierarchical three-body problem, and it was shown that GR effects suppress eccentricity in the parts of phase space where the GR timescales are several orders of magnitude shorter than the secular Newtonian one.
Journal ArticleDOI
Integrability and non-integrability in Hamiltonian mechanics
TL;DR: In this paper, the authors consider the problem of finding the topology of the state space of an integrable Hamiltonian system and prove its non-integrability in a neighbourhood of an equilibrium position.
Journal ArticleDOI
Aspects of the Hamiltonian dynamics of interacting gravitational gauge and Higgs fields with applications to spherical symmetry
TL;DR: In this article, the Hamiltonian dynamics of interacting gravitational Yang-Mills-Higgs fields are discussed and the main points of the general theory are illustrated and discussed in detail.
References
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Journal ArticleDOI
Forms of Relativistic Dynamics
TL;DR: In this paper, the authors combine the restricted principle of relativity with the hamiltonian formulation of dynamics, which leads to the appearance of ten fundamental quantities for each dynamical system, namely the total energy, the total momentum and the 6-vector which has three components equal to the total angular momentum.
Journal ArticleDOI
Homogeneous variables in classical dynamics
TL;DR: The well-known methods of classical mechanics, based on the use of a Lagrangian or Hamiltonian function, are adequate for the treatment of nearly all dynamical systems met with in practice.