23 citations · 66 across the 8 of their papers we have counts for
8 papers
Integrability of certain Hamiltonian systems in variable curvature spaces
Wojciech Szumiński, Adel A. Elmandouh
The objective of this work is to examine the integrability of Hamiltonian systems in spaces with variable curvature of certain types. Based on the differential Galois theory,…
Non-integrability of the Huang--Li nonlinear financial model
Wojciech Szumiński
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,\q…
Constrained N-body problems
Wojciech Szumiński, Maria Przybylska
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 an…
Note on integrability of certain homogeneous Hamiltonian systems
Wojciech Szumiński, A. J. Maciejewski, Maria Przybylska
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…
Analysis of constrained 2-body problem
Wojciech Szumiński, Tomasz Stachowiak
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 noni…
Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces
Andrzej J. Maciejewski, Wojciech Szumiński, Maria Przybylska
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 po…
Non-integrability of restricted double pendula
Tomasz Stachowiak, Wojciech Szumiński
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…
Non-integrability of flail triple pendulum
Maria Przybylska, Wojciech Szumiński
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…