Related papers: Contact variational integrators
We present a finite element variational integrator for compressible flows. The numerical scheme is derived by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the…
Simulation of contact and friction dynamics is an important basis for control- and learning-based algorithms. However, the numerical difficulties of contact interactions pose a challenge for robust and efficient simulators. A…
Dependable numerical results from long-time simulations require stable numerical integration schemes. For Hamiltonian systems, this is achieved with symplectic integrators, which conserve the symplectic condition and exactly solve for the…
A modern notion of integrability is that of multidimensional consistency (MDC), which classically implies the coexistence of (commuting) dynamical flows in several independent variables for one and the same dependent variable. This property…
In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states,…
The Teichm\"uller harmonic map flow, introduced in [9], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton--Jacobi theory for continuous contact…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to…
Multisymplectic variational integrators are structure preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and…
For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-dimensional systems, described by partial difference…
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable $z$. This provides a geometric framework for…
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to a…
We consider a frictional contact model, mathematically described by means of a nonlinear boundary value problem in terms of PDE. We draw the attention to three possible variational formulations of it. One of the variational formulations is…
The dynamical motion of mechanical systems possesses underlying geometric structures, and preserving these structures in numerical integration improves the qualitative accuracy and reduces the long-time error of the simulation. For a single…
We consider the continuous and discrete-time Hamilton's variational principle on phase space, and characterize the exact discrete Hamiltonian which provides an exact correspondence between discrete and continuous Hamiltonian mechanics. The…
In this paper we show, in a systematic way, how to relate the Kepler problem to the isotropic harmonic oscillator. Unlike previous approaches, our constructions are carried over in the Lagrangian formalism dealing with second order vector…
We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state and we approximate the action in a small…
The variation procedure on a teleparallel manifold is studied. The main problem is the non-commutativity of the variation with the Hodge dual map. We establish certain useful formulas for variations and restate the master formula due to…