Related papers: Nonholonomic Newmark method
This work deals with the solution of a non-convex optimization problem to enhance the performance of an energy harvesting device, which involves a nonlinear objective function and a discontinuous constraint. This optimization problem, which…
Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a…
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…
It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energy-diminishing methods to preserve…
We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…
In this article, it is experimentally verified that nonreciprocal photonic systems with a continuous translation symmetry may have an ill-defined topology. The topological classification of such systems is only feasible when the material…
We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations…
Hypothesis testing and other statistical inference procedures are most efficient when a reliable low-dimensional parametric family can be specified. We propose a method that learns such a family when one exists but its form is not known a…
In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate…
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced…
We propose a novel and systematic recurrence method for the energy spectra of non-Hermitian systems under open boundary conditions based on the recurrence relations of their characteristic polynomials. Our formalism exhibits better accuracy…
A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and…
We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying…
In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract…
We present a technique for calculating non-equilibrium Green functions for impurity systems with local interactions. We use an analogy to the calculation of response functions in the x-ray problem.The initial state and the final state…
In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the…
We present a general framework for constructing structure-preserving numerical integrators for nonholonomically constrained mechanical systems evolving on Lie groups using retraction maps. Retraction maps generalize the exponential map and…