Related papers: A note on Hybrid Routh reduction for time-dependen…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
In this paper we present a unified Lagrangian--Hamiltonian geometric formalism to describe time-dependent contact mechanical systems, based on the one first introduced by K. Kamimura and later formalized by R. Skinner and R. Rusk. This…
In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions…
The evolution of a Lagrangian mechanical system is variational. Likewise, when dealing with a hybrid Lagrangian system (a system with discontinuous impacts), the impacts can also be described by variations. These variational impacts are…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
In this paper we consider different model reduction techniques for systems with moving loads. Due to the time-dependency of the input and output matrices, the application of time-varying projection matrices for the reduction offers new…
In this paper we study the reductions of evolutionary PDEs on the manifold of the stationary points of time--dependent symmetries. In particular we describe how that the finite dimensional Hamiltonian structure of the reduced system is…
In this paper we study the reductions of evolutionary PDEs on the manifold of the stationary points of time-dependent symmetries. In particular we describe how the finite dimensional Hamiltonian structure of the reduced system is obtained…
In this paper we proved that under the Lazutkin's coordinate, the billiard map can be interpolated by a time-1 flow of a Hamiltonian $H(x,p,t)$ which can be formally expressed by \[…
A Lagrangian system with singularities is considered. The configuration space is a non-compact manifold that depends on time. A set of periodic solutions has been found.
When the Poincar\'{e} map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of a constant-dimensional invariant subsystem near the orbit which attracts all nearby…
It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that…
Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…
It is possible to introduce external time dependent back ground fields in the formulation of a system as fields whose dynamics can not be deduced from Euler Lagrange equations of motion. This method leads to singular Lagrangians for real…
Within the framework of Lagrangian mechanics, the conservativeness of the hydrostatic forces acting on a floating rigid body is proved. The representation of the associated hydrostatic potential is explicitly worked out. The invariance of…
This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
We consider a mechanical system which is controlled by means of moving constraints. Namely, we assume that some of the coordinates can be directly assigned as functions of time by means of frictionless constraints. This leads to a system of…
Hybrid dynamical systems pose significant challenges for effective planning and control, especially when additional constraints such as obstacle avoidance, state boundaries, and actuation limits are present. In this letter, we extend the…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…