Related papers: Variational integrators for electric circuits
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
We present a formulation of general nonlinear LC circuits within the framework of Birkhoffian dynamical systems on manifolds. We develop a systematic procedure which allows, under rather mild non-degeneracy conditions, to write the…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
In this work we construct a stochastic contact variational integrator and its discrete version via stochastic Herglotz variational principle for stochastic contact Hamiltonian systems. A general structure-preserving stochastic contact…
Discrete variational methods show excellent performance in numerical simulations of mechanical systems. In this paper, we adapt discrete variational integrators for the case of mechanical systems with double-bracket dissipation. In…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…
This paper explores the relationship between numerical integrators and optimal control algorithms. Specifically, the performance of the differential dynamical programming (DDP) algorithm is examined when a variational integrator and a newly…
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…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as…
Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed. This model features a noncanonical Hamiltonian formulation with a number of conserved…
We present a variational integrator based on the Lobatto quadrature for the time integration of dynamical systems issued from the least action principle. This numerical method uses a cubic interpolation of the states and the action is…
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and…
In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a…
Integrated photonic circuits play a crucial role in implementing quantum information processing in the noisy intermediate-scale quantum (NISQ) era. Variational learning is a promising avenue that leverages classical optimization techniques…
In this paper, we introduce two types of variational integrators, one originating from the discrete Hamilton's principle while the other from Galerkin variational approach. It turns out that these variational integrators are equivalent to…
The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy of a variational integrator with the order of approximation of the exact discrete Lagrangian by a computable…