Related papers: Focus-focus singularities in classical mechanics
We investigate local configuration controllability for mechanical control systems within the affine connection formalism. Extending the work by Lewis for the single-input case, we are able to characterize local configuration controllability…
We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
Singular Lagrangian fibrations arising from three-degree-of-freedom integrable Hamiltonian systems remain largely unexplored. While several results describe the global structure of large classes of systems with two degrees of freedom, only…
Some functorial and topological properties of vertical cohomologies and their application to completely integrable Hamiltonian systems are studied.
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real…
We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained…
A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are ``isolated'' near future time-like infinity or for a finite time interval. The underlying space-times need not admit a stationary…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
In a recent paper we have analyzed the role that a universal set of local symmetries plays in suppressing the superposition principle in classical mechanics via a path-integral formulation of classical mechanics itself. In this paper first…
In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials. First, following Han [2012] we develop a method to study…
For mechanical Hamiltonian systems on the torus, we study the dynamical properties of the generalized characteristics semiflows associated with certain Hamilton-Jacobi equations, and build the relation between the $\omega$-limit set of this…
We initiate the study of the classical mechanics of non-relativistic fractons in its simplest setting - that of identical one dimensional particles with local Hamiltonians characterized by by a conserved dipole moment in addition to the…
The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…
We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous…
In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the…
Interference dynamics is analyzed in the light of the complex quantum Hamilton-Jacobi formalism, using as a working model the collision of two Gaussian wave packets. Though simple, this model nicely shows that interference in quantum…
We show that any Hamiltonian system with one degree of freedom is invariant under a $w_\infty$ algebra of symmetries.