Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Szumiński, Wojciech"'
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability. They are gi
Externí odkaz:
http://arxiv.org/abs/2412.07310
Publikováno v:
W. Szumi\'nski, A.~J. Maciejewski, Dynamics and non-integrability of the double spring pendulum, J. Sound Vib., 589:118550, 2024
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 presents
Externí odkaz:
http://arxiv.org/abs/2406.02200
Autor:
Szumiński, Wojciech
This paper studies the dynamics and integrability of a variable-length coupled pendulum system. The complexity of the model is presented by joining various numerical methods, such as the Poincar\'e cross-sections, phase-parametric diagrams, and Lyapu
Externí odkaz:
http://arxiv.org/abs/2402.01224
Publikováno v:
Chaos 1 June 2023; 33 (6): 063156
Relativistic Hamiltonian equations describing a motion of a point mass in an arbitrary homogeneous potential are considered. For the first time, the necessary integrability conditions for integrability in the Liouville sense for this class of systems
Externí odkaz:
http://arxiv.org/abs/2307.10070
Autor:
Szumiński, Wojciech
In this paper we consider Huang--Li nonlinear financial system recently studied in the literature. It has the form of three first order differential equations \[ \dot x=z+(y-a)x,\quad \dot y=1-b y-x^2,\quad \dot z=-x-c z, \] where $(a,b,c)$ are real
Externí odkaz:
http://arxiv.org/abs/1703.06623
Two versions of the semi-classical Jaynes--Cummings model without the rotating wave approximation are investigated. It is shown that for a non-zero value of the coupling constant the version introduced by Belobrov, Zaslavsky, and Tartakovsky is Hamil
Externí odkaz:
http://arxiv.org/abs/1703.06625
Autor:
Szumiński, Wojciech, Przybylska, Maria
We consider a problem of mass points interacting gravitationally whose motion is subjected to certain holonomic constraints. The motion of points is restricted to certain curves and surfaces. We illustrate the complicated behaviour of trajectories of
Externí odkaz:
http://arxiv.org/abs/1606.03204
Publikováno v:
Phys. Lett. A, vol. 379 no 45-46, 2970-2976, 2015
In this paper we investigate a class of natural Hamiltonian systems with two degrees of freedom. The kinetic energy depends on coordinates but the system is homogeneous. Thanks to this property it admits, in a general case, a particular solution. Usi
Externí odkaz:
http://arxiv.org/abs/1606.03023
Publikováno v:
Applied Non-Linear Dynamical Systems, ed. Jan Awrejcewicz, Springer Proceedings in Mathematics & Statistics 182, pp. 361-372, 2016
We consider the system of two material points that interact by elastic forces according to Hooke's law and their motion is restricted to certain curves lying on the plane. The nonintegrability of this system and idea of the proof are communicated. Mo
Externí odkaz:
http://arxiv.org/abs/1606.03009
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 potential
Externí odkaz:
http://arxiv.org/abs/1606.01084