Related papers: Non-integrability of the generalised spring-pendul…
In this paper we analyze the non-integrability of the Wilbeforce pendulum by means of Morales-Ramis theory in where is enough to prove that the Galois group of the variational equation is not virtually abelian. We obtain these…
We consider a special type of triple pendulum with two pendula attached to end mass of another one. Although we consider this system in the absence of the gravity, a quick analysis of of Poincar\'e cross sections shows that it is not…
We consider the problem of $n$ points with positive masses interacting pairwise with forces inversely proportional to the distance between them. In particular, it is the classical gravitational, Coulomb or photo-gravitational $n$-body…
We show the non-integrability of the three-parameter Armburster-Guckenheimer-Kim quartic Hamiltonian using Morales-Ramis theory, with the exception of the three already known integrable cases. We use Poincar\'e sections to illustrate the…
This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Hamiltonian system with three degrees of freedom, its analysis…
This paper examines the quantum mechanical system that arises when one quantises a classical mechanical configuration described by an underdetermined system of equations. Specifically, we consider the well-known problem in classical…
We prove that the Ziegler pendulum -- a double pendulum with a follower force -- can be integrable, provided that the stiffness of the elastic spring located at the pivot point of the pendulum is zero and there is no friction in the system.…
The basic theory of Differential Galois and in particular Morales--Ramis theory is reviewed with focus in analyzing the non--integrability of various problems of few bodies in Celestial Mechanics. The main theoretical tools are:…
In this paper we study the integrability of the Sasano system of type $A^{(2)}_4$ from the point of view of the Hamiltonian dynamics. We prove rigorously that for these values of the parameters for which the Sasano system of type…
Let $V\in\mathbb{Q}(i)(\a_1,\dots,\a_n)(\q_1,\q_2)$ be a rationally parametrized planar homogeneous potential of homogeneity degree $k\neq -2, 0, 2$. We design an algorithm that computes polynomial \emph{necessary} conditions on the…
In recent papers by the authors (S.~Motonaga and K.~Yagasaki, Obstructions to integrability of nearly integrable dynamical systems near regular level sets, submitted for publication, and K.~Yagasaki, Nonintegrability of nearly integrable…
This is an example of application of Ziglin-Morales-Ramis algebraic studies in Hamiltonian integrability, more specifically the result by Morales, Ramis and Sim\'o on higher-order variational equations, to the well-known…
We prove that the classical planar $n$-body problem when restricted to a common level of the energy and the angular momentum is not integrable except in the case when both values of these integrals are zero. In the proof of our theorem, we…
We consider two special types of double pendula, with the motion of masses restricted to various surfaces. In order to get quick insight into the dynamics of the considered systems the Poincar\'e cross sections as well as bifurcation…
We study the integrability of the Hamiltonian normal form of 1 : 2 : 2 resonance. It is known that this normal form truncated to order three is integrable. The truncated to order four normal form contains too many parameters. For a generic…
The aim of this study is to analyze the integrability problem of Lotka--Volterra three species biological system. The system which considered in this work is a biological plausibility or a chemical model. The system has a complex dynamical…
We consider conformation dynamics of a chain-like three-body bead-spring model, in which three point masses are connected in series by two springs and the conformation is defined by the bending angle between the two springs. Previous…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
Driven by breakthroughs in experimental and theoretical techniques, the study of non-equilibrium quantum physics is a rapidly expanding field with many exciting new developments. Amongst the manifold ways the topic can be investigated, one…
The Sasano sytem of type $A^{(2)}_5$ is a four-dimensional non-linear system of ordinary differential equations, which has an affine Weyl group of symmetries of type $A^{(2)}_5$. It is also a tipe dependent Hamiltonian system, which can be…