Related papers: Feedback Integrators
Roadheader is an engineering robot widely used in underground engineering and mining industry. Interactive dynamics simulation of roadheader is a fundamental problem in unmanned excavation and virtual reality training. However, current…
We derive nonlinear stability results for numerical integrators on Riemannian manifolds, by imposing conditions on the ODE vector field and the step size that makes the numerical solution non-expansive whenever the exact solution is…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
Expositions of the Euler equations for the rotation of a rigid body often invoke the idea of a specially damped system whose energy dissipates while its angular momentum magnitude is conserved in the body frame. An attempt to explicitly…
Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about rigid-body dynamics in the presence…
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 the…
Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
In this paper we consider discrete gradient methods for approximating the solution and preserving a first integral (also called a constant of motion) of autonomous ordinary differential equations. We prove under mild conditions for a large…
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
We calculate Noether like operators and first integrals of scalar equation y'' = -k^2 y using complex Lie symmetry method, by taking values of k and y to be real as well as complex. We numerically integrate the equations using a symplectic…
The notion of feedback integrators permits Euclidean integration schemes for dynamical systems evolving on manifolds. Here, a constructive Lyapunov function for the attitude dynamics embedded in an ambient Euclidean space has been proposed.…