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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Book ChapterDOI
The Delauney-Dubins Problem
TL;DR: In this paper, the key equation in the problem of Delauney, obtained by Josepha Von Schwartz in mid 1930s also appears in the spacial version of Dubins, and the optimal solutions in the plane are the concatenations of circles of curvature ±c and straight lines with at most two switchings from one arc to another.
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The Homology Class of a Poisson Transversal
Pedro Frejlich,Ioan Marcut +1 more
TL;DR: In this article, the homology class of compact Poisson transversal in a Poisson manifold is studied, and it is shown that these transversals represent non-trivial homology classes.
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Dirac Quantization of t’Hooft-Polyakov Monopole Field: Axial Hamiltonization
TL;DR: In this article, the axial gauge of the t'Hooft-Polyakov monopole field outside the localized region, which represents the monopole's core, was Hamiltonized.
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Hamilton-Jacobi Quantization of Singular Lagrangians with Linear Velocities
TL;DR: In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton-Jacobi method, where integrablity conditions are considered on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians.
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Instant-form Hamiltonian and Becchi-Rouet-Stora-Tyutin formulations of the Nielsen-Olesen model in the broken symmetry phase
TL;DR: In this article, the usual instant-form (equal-time) Hamiltonian and Becchi−RouetStoraTyutin formulations of the NielsenOlesen model are investigated in two-space one-time dimension in the broken (frozen) symmetry phase, where the phase ϕ(xμ) of the complex matter field Φ(x) carries the charge degree of freedom of the field and is, in fact, akin to the Goldstone boson.
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.