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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Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories
TL;DR: In this article, it was shown that the k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description.
Journal ArticleDOI
Nonequilibrium Steady States and Fano-Kondo Resonances in an AB Ring with a Quantum Dot
Junko Takahashi,Shuichi Tasaki +1 more
TL;DR: In this paper, a nonequilibrium steady state of the mean-field Hamiltonian was constructed with the aid of the C*-algebraic approach for studying infinitely extended systems.
Journal ArticleDOI
Morse families and Dirac systems
TL;DR: In this paper, an integrability algorithm in the sense of Mendela, Marmo and Tulczyjew is described for the generalized Dirac dynamical systems under study to determine the set where the implicit differential equations have solutions.
Journal ArticleDOI
On the Hamiltonian formalism for general Lagrangians with higher-order derivatives
Journal ArticleDOI
Invariant Lagrangian Theory of the Poisson Bracket for Systems with Constraints
TL;DR: In this article, a universal theory of the Poisson bracket and its Fermi-Dirac counterpart for Lagrangian dynamical systems with arbitrarily complicated constraint structure is presented.
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.