In this paper, we describe a geometric setting for higher-order Lagrangian problems on Lie
groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an …

Numerical methods that preserve geometric invariants of the system, such as energy,
momentum or the symplectic form, are called geometric integrators. In this paper we present …

High-Order Splines on Riemannian Manifolds | SpringerLink Skip to main content Advertisement
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Proceedings …

We present a new class of high-order variational integrators on Lie groups. We show that
these integrators are symplectic and momentum-preserving, can be constructed to be of …

In this paper we develop a geometric approach to higher order mechanics on graded
bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered …

In this paper, we study simple splines on a Riemannian manifold $ Q $ from the point of view
of the Pontryagin maximum principle (PMP) in optimal control theory. The control problem …

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 …

An interesting family of geometric integrators for Lagrangian systems can be defined using
discretizations of the Hamilton's principle of critical action. This family of geometric …

In this paper we investigate a variational discretization for the class of mechanical systems in
presence of symmetries described by the action of a Lie group which reduces the phase …

Variational integrators for dynamic systems with holonomic constraints are proposed based
on Hamilton's principle. The variational principle is discretized by approximating the …