27 research outputs found
On a class of three dimensional quadratic Hamiltonian systems
The purpose of this article is to compute the normal form of a class of
general quadratic Hamiltonian systems that generalizes naturally Euler's
equations from the free rigid body dynamics.Comment: 6 page
A short proof of chaos in an atmospheric system
We will prove the presence of chaotic motion in the Lorenz five-component
atmospheric system model using the Melnikov function method developed by Holmes
and Marsden for Hamiltonian systems on Lie Groups.Comment: PACS: 02.20.Sv; 02.30.Hg; 02.40.-k; 92.60.-e. 5 page
On a unified formulation of completely integrable systems
The purpose of this article is to show that a differential
system on which admits a set of independent
conservation laws defined on an open subset , is
essentially equivalent on an open and dense subset of ,
with the linear differential system $u^\prime_1=u_1, \ u^\prime_2=u_2,..., \
u^\prime_n=u_n$. The main results are illustrated in the case of two concrete
dynamical systems, namely the three dimensional Lotka-Volterra system, and
respectively the Euler equations from the free rigid body dynamics.Comment: 11 page
Periodic orbits in the case of a zero eigenvalue
We will show that if a dynamical system has enough constants of motion then a
Moser-Weinstein type theorem can be applied for proving the existence of
periodic orbits in the case when the linearized system is degenerate.Comment: 6 pages, no figure
Symmetry breaking for toral actions in simple mechanical systems
For simple mechanical systems, bifurcating branches of relative equilibria
with trivial symmetry from a given set of relative equilibria with toral
symmetry are found. Lyapunov stability conditions along these branches are
given.Comment: 25 page
The free rigid body dynamics: generalized versus classic
In this paper we analyze the normal forms of a general quadratic Hamiltonian
system defined on the dual of the Lie algebra of real -
skew - symmetric matrices, where is an arbitrary real symmetric
matrix. A consequence of the main results is that any first-order autonomous
three-dimensional differential equation possessing two independent quadratic
constants of motion which admits a positive/negative definite linear
combination, is affinely equivalent to the classical "relaxed" free rigid body
dynamics with linear controls.Comment: 12 page
Complete integrability versus symmetry
The purpose of this article is to show that on an open and dense set,
complete integrability implies the existence of symmetry