On third order integrable vector Hamiltonian equations

Integrable Hamiltonian Systems with Vector Potentials

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of weakly-integrable systems. In the case of a quadratic second invariant, we recover the classical strongly-integrable systems in Cartesian and polar coordinate...

Instability Results for Certain Third Order Nonlinear Vector Differential Equations

Our goal in this paper is to obtain sufficient conditions for instability of the zero solution to the non-linear vector differential equation ... X + F (X, Ẋ)Ẍ + G(Ẋ) + H(X) = 0. An example illustrates the results obtained.

Some Instability Results on Certain Third Order Nonlinear Vector Differential Equations

In this paper, we obtain some sufficient conditions under which the zero solution of a certain third order non-linear ordinary vector differential equation is unstable. Our results include and improve some well-known results exist in the literature.

Second order hamiltonian vector fields on tangent bundles

Let M be a differentiable manifold. A vector field Γ of TM which corresponds to a system of second order ordinary differential equations on M is called a second order Hamiltonian vector field if it is the Hamiltonian field of a function F ∈ C∞(TM) with respect to a Poisson structure P of TM . We formulate the direct problem as that of finding Γ if P is given, and the inverse problem as that of ...

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS