Related papers: Variational integrators for underactuated mechanic…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
Variational integrators are a special kind of geometric discretisation methods applicable to any system of differential equations that obeys a Lagrangian formulation. In this thesis, variational integrators are developed for several…
The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Essentially, we prove that when a discretization of contact order $r$ of the Lagrangian and force…
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…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
We deliver a novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping by establishing a restricted Hamilton's principle. Fractional damping is a particular instance of non-local (in…
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…
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…
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…
In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…
Discrete Hamiltonian variational integrators are derived from Type II and Type III generating functions for symplectic maps, and in this paper we establish a variational error analysis result that relates the order of accuracy of the…
In this paper we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for…
Forced variational integrators are given by the discretization of the Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical simulation studies of complex dynamical systems. In this paper…
We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent bundles, ${\rm…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
In this paper structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton-Pontryagin variational principle. From this principle one can derive a novel class of variational partitioned…
We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a contact transformation and that any contact map can be…