86 citations · 631 across the 43 of their papers we have counts for
14 papers · 1 filter
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…
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…
The inhomogeneous Suslov problem
Luis C. García-Naranjo, Andrzej J. Maciejewski, Juan C. Marrero +1
We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perp…
The generalized Euler-Poinsot rigid body equations: explicit elliptic solutions
Yuri N. Fedorov, Andrzej J. Maciejewski, Maria Przybylska
The classical Euler--Poinsot case of the rigid body dynamics admits a class of simple but non-trivial integrable generalizations, which modify the Poisson equations describing the…
Darboux Points and Integrability Analysis of Hamiltonian Systems with Homogeneous Rational Potentials
Michał Studziński, Maria Przybylska
We study the integrability in the Liouville sense of natural Hamiltonian systems with a homogeneous rational potential $V(\vq)$. Strong necessary conditions for the integrability o…
On algebraic construction of certain integrable and super-integrable systems
Andrzej. J. Maciejewski, Maria Przybylska, Andrey V. Tsiganov
We propose a new construction of two-dimensional natural bi-Hamiltonian systems associated with a very simple Lie algebra. The presented construction allows us to distinguish three…
Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces
Andrzej J. Maciejewski, Maria Przybylska, Haruo Yoshida
We formulate the necessary conditions for the maximal super-integrability of a certain family of classical potentials defined in the constant curvature two-dimensional spaces. We g…
Differential Galois theory and Integrability
Andrzej J. Maciejewski, Maria Przybylska
This paper is an overview of our works which are related to investigations of the integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations wi…
Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom. Nongeneric cases
Maria Przybylska
In this paper the problem of classification of integrable natural Hamiltonian systems with degrees of freedom given by a Hamilton function which is the sum of the standard kine…
Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom
Maria Przybylska
We consider natural complex Hamiltonian systems with degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomi…
Differential Galois obstructions for non-commutative integrability
Andrzej J. Maciejewski, Maria Przybylska
We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at…
Finiteness of integrable -dimensional homogeneous polynomial potentials
Maria Przybylska
We consider natural Hamiltonian systems of degrees of freedom with polynomial homogeneous potentials of degree . We show that under a genericity assumption, for a fixed $k…
Differential Galois obstructions for integrability of homogeneous Newton equations
Maria Przybylska
n this paper we formulate necessary conditions for the integrability in the Jacobi sense of Newton equations $\ddot \vq=-\vF(\vq)$, where $\vq\in\C^n$ and all components of $\vF$ a…
Necessary conditions for partial and super-integrability of Hamiltonian systems with homogeneous potentia
Andrzej J. Maciejewski, Maria Przybylska, Haruo Yoshida
We consider a natural Hamiltonian system of degrees of freedom with a homogeneous potential. Such system is called partially integrable if it admits independent and com…