23 research outputs found
Multisymplectic Lie group variational integrator for a geometrically exact beam in R3
In this paper we develop, study, and test a Lie group multisymplectic
integra- tor for geometrically exact beams based on the covariant Lagrangian
formulation. We exploit the multisymplectic character of the integrator to
analyze the energy and momentum map conservations associated to the temporal
and spatial discrete evolutions.Comment: Article in press. 22 pages, 18 figures. Received 20 November 2013,
Received in revised form 26 February 2014, Accepted 27 February 2014.
Communications in Nonlinear Science and Numerical Simulation. 201
Discrete Variational Optimal Control
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 variational principles. The key point is to solve the optimal control
problem as a variational integrator of a specially constructed
higher-dimensional system. The developed framework applies to systems on
tangent bundles, Lie groups, underactuated and nonholonomic systems with
symmetries, and can approximate either smooth or discontinuous control inputs.
The resulting methods inherit the preservation properties of variational
integrators and result in numerically robust and easily implementable
algorithms. Several theoretical and a practical examples, e.g. the control of
an underwater vehicle, will illustrate the application of the proposed
approach.Comment: 30 pages, 6 figure