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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Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics
TL;DR: In this article, the authors argue that the source of the problem can be found precisely within the symplectic reduction that goes along with strict adherence to the Dirac view, and propose alternative strategies for dealing with Hamiltonian constraints.
Journal ArticleDOI
On singular Lagrangians affine in velocities
TL;DR: The properties of Lagrangians affine in velocities are analyzed in a geometric way in this article, and the analysis of constraint functions and gauge symmetry leads to a complete classification of such Lagrangian affine systems.
Journal ArticleDOI
Horizons, constraints, and black hole entropy
TL;DR: In this paper, it was shown that the notion of a "stretched horizon" constraint modifies the algebra of symmetries at the horizon, allowing the use of standard conformal field theory techniques to determine the asymptotic density of states.
Journal ArticleDOI
Quantization of nonlinear sigma model in constrained hamiltonian formalism
TL;DR: In this paper, the canonical structure and quantization of the O(N) nonlinear sigma model in the constrained hamiltonian formalism due to Dirac were investigated, and the explicit form of the quantum hamiltonians of this model was obtained.
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.