---
_id: '16630'
abstract:
- lang: eng
  text: <jats:p>This paper formulates the dynamical equations of mechanics subject
    to holonomic constraints in terms of the states and controls using a constrained
    version of the Lagrange-d’Alembert principle. Based on a discrete version of this
    principle, a structure preserving time-stepping scheme is derived. It is shown
    that this respect for the mechanical structure (such as a reliable computation
    of the energy and momentum budget, without numerical dissipation) is retained
    when the system is reduced to its minimal dimension by the discrete null space
    method. Together with initial and final conditions on the configuration and conjugate
    momentum, the reduced time-stepping equations serve as nonlinear equality constraints
    for the minimisation of a given cost functional. The algorithm yields a sequence
    of discrete configurations together with a sequence of actuating forces, optimally
    guiding the system from the initial to the desired final state. The resulting
    discrete optimal control algorithm is shown to have excellent energy and momentum
    properties, which are illustrated by two specific examples, namely reorientation
    and repositioning of a rigid body subject to external forces and the reorientation
    of a rigid body with internal momentum wheels.</jats:p>
author:
- first_name: Sigrid
  full_name: Leyendecker, Sigrid
  last_name: Leyendecker
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  last_name: Ober-Blöbaum
- first_name: Jerrold E.
  full_name: Marsden, Jerrold E.
  last_name: Marsden
- first_name: Michael
  full_name: Ortiz, Michael
  last_name: Ortiz
citation:
  ama: 'Leyendecker S, Ober-Blöbaum S, Marsden JE, Ortiz M. Discrete Mechanics and
    Optimal Control for Constrained Multibody Dynamics. In: <i>Volume 5: 6th International
    Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B,
    and C</i>. ; 2007. doi:<a href="https://doi.org/10.1115/detc2007-34574">10.1115/detc2007-34574</a>'
  apa: 'Leyendecker, S., Ober-Blöbaum, S., Marsden, J. E., &#38; Ortiz, M. (2007).
    Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics. In
    <i>Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics,
    and Control, Parts A, B, and C</i>. <a href="https://doi.org/10.1115/detc2007-34574">https://doi.org/10.1115/detc2007-34574</a>'
  bibtex: '@inproceedings{Leyendecker_Ober-Blöbaum_Marsden_Ortiz_2007, title={Discrete
    Mechanics and Optimal Control for Constrained Multibody Dynamics}, DOI={<a href="https://doi.org/10.1115/detc2007-34574">10.1115/detc2007-34574</a>},
    booktitle={Volume 5: 6th International Conference on Multibody Systems, Nonlinear
    Dynamics, and Control, Parts A, B, and C}, author={Leyendecker, Sigrid and Ober-Blöbaum,
    Sina and Marsden, Jerrold E. and Ortiz, Michael}, year={2007} }'
  chicago: 'Leyendecker, Sigrid, Sina Ober-Blöbaum, Jerrold E. Marsden, and Michael
    Ortiz. “Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics.”
    In <i>Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics,
    and Control, Parts A, B, and C</i>, 2007. <a href="https://doi.org/10.1115/detc2007-34574">https://doi.org/10.1115/detc2007-34574</a>.'
  ieee: 'S. Leyendecker, S. Ober-Blöbaum, J. E. Marsden, and M. Ortiz, “Discrete Mechanics
    and Optimal Control for Constrained Multibody Dynamics,” in <i>Volume 5: 6th International
    Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B,
    and C</i>, 2007.'
  mla: 'Leyendecker, Sigrid, et al. “Discrete Mechanics and Optimal Control for Constrained
    Multibody Dynamics.” <i>Volume 5: 6th International Conference on Multibody Systems,
    Nonlinear Dynamics, and Control, Parts A, B, and C</i>, 2007, doi:<a href="https://doi.org/10.1115/detc2007-34574">10.1115/detc2007-34574</a>.'
  short: 'S. Leyendecker, S. Ober-Blöbaum, J.E. Marsden, M. Ortiz, in: Volume 5: 6th
    International Conference on Multibody Systems, Nonlinear Dynamics, and Control,
    Parts A, B, and C, 2007.'
date_created: 2020-04-16T08:28:13Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1115/detc2007-34574
language:
- iso: eng
publication: 'Volume 5: 6th International Conference on Multibody Systems, Nonlinear
  Dynamics, and Control, Parts A, B, and C'
publication_identifier:
  isbn:
  - 079184806X
publication_status: published
status: public
title: Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics
type: conference
user_id: '15701'
year: '2007'
...