相关论文: Weak-Hamiltonian dynamical systems
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…
In this paper we extend the previously introduced class of boundary port-Hamiltonian systems to boundary control systems where the variational derivative of the Hamiltonian functional is replaced by a pair of reciprocal differential…
We consider a recent formulation of weak KAM theory proposed by Evans. As well as for classical integrability, for one dimensional mechanical Hamiltonian systems all the computations can be explicitly done. This allows us on the one hand to…
We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
The anisotropic and heterogeneous $N$-dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system. A recent structure-preserving mixed Galerkin method is applied, leading directly to a…
In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly,…
A point-like object moving in a background black hole spacetime experiences a gravitational self-force which can be expressed as a local function of the object's instantaneous position and velocity, to linear order in the mass ratio. We…
The {\it curvature} and the {\it reduced curvature} are basic differential invariants of the pair: (Hamiltonian system, Lagrange distribution) on the symplectic manifold. We show that negativity of the curvature implies that any bounded…
We consider $\mathcal{PT}$-symmetric ring-like arrays of optical waveguides with purely nonlinear gain and loss. Regardless of the value of the gain-loss coefficient, these systems are protected from spontaneous $\mathcal{PT}$-symmetry…
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…
We will give general sufficient conditions under which a controller achieves robust regulation for a boundary control and observation system. Utilizing these conditions we construct a minimal order robust controller for an arbitrary order…
In order to describe the impact of different geometric structures and constraints for the dynamics of a Hamiltonian system, in this paper, for a magnetic Hamiltonian system defined by a magnetic symplectic form, we first drive precisely the…
This is an expository paper on Lyapunov stability of equilibria of autonomous Hamiltonian systems. Our aim is to clarify the concept of weak instability, namely instability without non-constant motions which have the equilibrium as limit…
We study Hamiltonian systems near a compact symplectic Morse-Bott minimum. Our first result shows that if the flow is Zoll (that is, it induces a free circle action) along a sequence of energy levels converging to the minimum, then the…
We extend the modeling framework of port-Hamiltonian descriptor systems to include under- and over-determined systems and arbitrary differentiable Hamiltonian functions. This structure is associated with a Dirac structure that encloses its…
Port-Hamiltonian systems provide an energy-based formulation with a model class that is closed under structure preserving interconnection. For continuous-time systems these interconnections are constructed by geometric objects called Dirac…
This work introduces a port-Hamiltonian (PH) model for constrained mechanical systems, which is directly derived from the Lagrangian equations of motion. The present PH framework incorporates a singularity-free director representation of…
We extend the port-Hamiltonian framework defined with respect to a Lagrangian submanifold and a Dirac structure by augmenting the Lagrangian submanifold with the space of external variables. The new pair of conjugated variables is called…
We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as…