Related papers: Simulating Nonholonomic Dynamics
In this paper, we will discuss new developments regarding the Geometric Nonholonomic Integrator (GNI) [23, 24]. GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was…
In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…
A geometric derivation of nonholonomic integrators is developed. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems. The theoretical methodology and the integrators…
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…
In this paper we explore the nonholonomic Lagrangian setting of mechanical systems in local coordinates on finite-dimensional configuration manifolds. We prove existence and uniqueness of solutions by reducing the basic equations of motion…
In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the…
In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a…
We construct the exponential map associated to a nonholonomic system that allows us to define an exact discrete nonholonomic constraint submanifold. We reproduce the continuous nonholonomic flow as a discrete flow on this discrete…
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of…
We introduce energy-preserving integrators for nonholonomic mechanical systems. We will see that the nonholonomic dynamics is completely determined by a triple $({\mathcal D}^*, \Pi, \mathcal{H})$, where ${\mathcal D}^*$ is the dual of the…
We propose a numerical scheme for the time-integration of nonholonomic mechanical systems, both conservative and nonconservative. The scheme is obtained by simultaneously discretizing the constraint equations and the Herglotz variational…
We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on…
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…
In this paper we study a Hamiltonization procedure for mechanical systems with velocity-depending (nonholonomic) constraints. We first rewrite the nonholonomic equations of motion as Euler-Lagrange equations, with a Lagrangian that follows…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of 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…
Geometric integration of non-autonomous classical engineering problems, such as rotor dynamics, is investigated. It is shown, both numerically and by backward error analysis, that geometric (structure preserving) integration algorithms are…