Related papers: Integrable systems in planar robotics
In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.
A three-vortex system on a plane is known to be minimally superintegrable in the Liouville sense. In this work, integrable generalisations of the three-vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It…
Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…
This note constructs completely integrable convex Hamiltonians on the cotangent bundle of certain k-dimensional torus bundles over an l-dimensional torus. A central role is played by the Lax representation of a Bogoyavlenskij-Toda lattice.…
In (1+1)-dimensional quantum field theory, integrability is typically defined as the existence of an infinite number of local charges of different Lorentz spin, which commute with the Hamiltonian. A well known consequence of integrability…
Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it…
We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems…
Using the procedure of the marked point fusion, there are obtained integrable systems with poles in the matrix of the Lax operator order higher than one, considered Hamiltonians, symplectic structure and symmetries of these systems. Also,…
Construction and classification of 2D superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of…
This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect…
As robots become increasingly prominent in diverse industrial settings, the desire for an accessible and reliable system has correspondingly increased. Yet, the task of meaningfully assessing the feasibility of introducing a new robotic…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Recently one integrable model with a cubic first integral of motion has been studied by Valent using some special coordinate system. We describe the bi-Hamiltonian structures and variables of separation for this system.
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko-Fomenko theorem on noncommutative…
The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system…
It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian…
We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew…
This paper presents a computational model of the processing of dynamic spatial relations occurring in an embodied robotic interaction setup. A complete system is introduced that allows autonomous robots to produce and interpret dynamic…