On Second Order Hamiltonian Systems
نویسندگان
چکیده
The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.
منابع مشابه
Balanced Truncation of Linear Second-Order Systems: A Hamiltonian Approach
We present a formal procedure for structure-preserving model reduction of linear second-order and Hamiltonian control problems that appear in a variety of physical contexts, e.g., vibromechanical systems or electrical circuit design. Typical balanced truncation methods that project onto the subspace of the largest Hankel singular values fail to preserve the problem’s physical structure and may ...
متن کاملNew conditions on ground state solutions for Hamiltonian elliptic systems with gradient terms
This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...
متن کاملOn periodic solutions of nonautonomous second order Hamiltonian systems with ( q , p ) - Laplacian
A new existence result is obtained for nonautonomous second order Hamiltonian systems with (q, p)-Laplacian by using the minimax methods.
متن کاملExistence of Homoclinic Solutions for Second Order Hamiltonian Systems under Local Conditions
Under some local conditions on V(t,x) with respect to x , the existence of homoclinic solutions is obtained for a class of the second order Hamiltonian systems ü(t) +∇V(t,u(t)) = f (t), ∀t ∈ R .
متن کاملSymplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects
In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...
متن کامل