Related papers: AKS systems and Lepage equivalent problems
A heavy top with a fixed point and a rigid body in an ideal fluid are important examples of Hamiltonian systems on a dual to the semidirect product Lie algebra $e(n)=so(n)\ltimes\mathbb R^n$. We give a Lagrangian derivation of the…
In this paper, variational techniques are used to analyze the dynamics of nonholonomic mechanical systems with impacts. Implicit nonholonomic smooth Lagrangian and Hamiltonian systems are extended to a nonsmooth context appropriate for…
For the super AKNS system, an implicit symmetry constraint between the potentials and the eigenfunctions is proposed. After introducing some new variables to explicitly express potentials, the super AKNS system is decomposed into two…
It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamiltonian. We investigate this property from the variational…
Quantum computation has suggested, among others, the consideration of "non-quantum" systems which in certain respects may behave "quantum-like". Here, what algebraically appears to be the most general possible known setup, namely, of {\it…
The quantum $H_3$ integrable system is a 3D system with rational potential related to the non-crystallographic root system $H_3$. It is shown that the gauge-rotated $H_3$ Hamiltonian as well as one of the integrals, when written in terms of…
We provide a symplectic reduction of a partially integrable Hamiltonian system to a completely integrable one. The KAM theorem is applied to this reduced completely integrable Hamiltonian system. Its KAM perturbation generates a…
The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.
A novel functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The new approach, which we call "stringy quantization," is based solely on classical equations of motion and is free of any ambiguity…
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence…
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised. The relationship with the Lie-algebraic integrability…
In this paper we present a novel construction of non-homogeneous hydrodynamic equations from what we call quasi-St\"ackel systems, that is non-commutatively integrable systems constructed from appropriate maximally superintegrable St\"ackel…
The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric…
In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature.…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…
A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and…
Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the…
Hex systems were recently introduced [A. P. Kels. Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces. 2022. arXiv:2205.02720 [math-ph]] as systems of equations defined on…
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…