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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Journal ArticleDOI
Dynamical systems with first- and second-class constraints. II. Local-symmetry transformations
TL;DR: In this article, the authors investigated local symmetries of dynamical systems with first-and second-class constraints and showed that the degeneracy of these theories is due to their invariance under local symmetry transformations.
Journal ArticleDOI
Variational Discretizations of Gauge Field Theories Using Group-Equivariant Interpolation
TL;DR: A systematic mathematical approach to the geometric discretization of gauge field theories that is based on Dirac and multi-Dirac mechanics and geometry is described, which provide a unified mathematical framework for describing Lagrangian and Hamiltonian mechanics and field theories.
Posted Content
The Hopfield model revisited: Covariance and Quantization
TL;DR: In this article, the Hopfield model for the electromagnetic field in dielectric dispersive medium is extended with mesoscopic parameters, such as susceptibility, resonance frequency, and coupling between electromagnetic field and polarization field.
Journal ArticleDOI
Treatment of the classical relativistic string in any orthonormal gauge
TL;DR: In this article, it was shown that a certain set of gauge invariant functions are, for an appropriate choice of a parameter on which they depend, equal to the Fourier components of the classical relativistic string in any orthonormal gauge.
Book ChapterDOI
Adiabatic Invariance in Volume-Preserving Systems
TL;DR: In this article, the authors consider the destruction of adiabatic invariance in volume-preserving systems due to separatrix crossings, scattering on and capture into resonances, which result in mixing and transport in large domains of phase space.
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.