Related papers: Asynchronous Variational Contact Mechanics
Asynchronous Variational Integrators (AVIs) have demonstrated long-time good energy behavior. It was previously conjectured that this remarkable property is due to their geometric nature: they preserve a discrete multisymplectic form.…
The phase field approach is widely used to model fracture behaviors due to the absence of the need to track the crack topology and the ability to predict crack nucleation and branching. In this work, the asynchronous variational integrators…
Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…
Formation control of autonomous agents can be seen as a physical system of individuals interacting with local potentials, and whose evolution can be described by a Lagrangian function. In this paper, we construct and implement forced…
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…
In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering the dynamics of an electrical circuit, one is faced with three special situations: 1. The system…
Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
One approach to analyzing the dynamics of a physical system is to search for long-lived patterns in its motions. This approach has been particularly successful for molecular dynamics data, where slowly decorrelating patterns can indicate…
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by the use of mixed finite elements and discrete differential…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method…
This paper presents a method to construct variational integrators for time-dependent lagrangian systems. The resulting algorithms are symplectic, preserve the momentum map associated with a Lie group of symmetries and also describe the…
A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…
We present an efficient spacetime optimization method to automatically generate animations for a general volumetric, elastically deformable body. Our approach can model the interactions between the body and the environment and automatically…
The goal of this paper is to develop energy-preserving variational integrators for time-dependent mechanical systems with forcing. We first present the Lagrange-d'Alembert principle in the extended Lagrangian mechanics framework and derive…
Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the…