---
_id: '63765'
abstract:
- lang: eng
  text: Rubber-metal bushings (RMB) are critical components in multi-body systems,
    such as vehicles and industrial machinery, due to their ability to enable relative
    motion, dampen vibrations, and transmit forces. However, their nonlinear behavior
    challenges accurate modeling. Traditional physics-based models often fail to balance
    simplicity, accuracy, and computational efficiency. The growing availability of
    experimental data offers opportunities to improve RMB modeling through hybrid
    and data-driven approaches. This study evaluates physics-based, hybrid, and data-driven
    methods based on predictive accuracy, modeling effort, and computational cost.
    Hybrid approaches, combining machine learning techniques with physics-based models,
    are investigated to leverage their complementary strengths. Results show that
    hybrid methods enhance accuracy for simpler models with a modest increase in computational
    time. This highlights their potential to simplify RMB modeling while balancing
    accuracy and efficiency, offering insights for advancing multi-body system simulations.
    Building on these insights, data-driven methods are explored for their ability
    to provide surrogate models for dynamical systems without requiring expert knowledge.
    Experiments reveal that while simple data-driven methods approximate system behavior
    when data has low variance, they fail with trajectories of widely varying frequency
    and amplitude.
author:
- first_name: Meike Claudia
  full_name: Wohlleben, Meike Claudia
  id: '43991'
  last_name: Wohlleben
  orcid: 0009-0009-9767-7168
- first_name: Jan
  full_name: Schütte, Jan
  id: '22109'
  last_name: Schütte
  orcid: 0000-0001-9025-9742
- first_name: Manuel Bastian
  full_name: Berkemeier, Manuel Bastian
  last_name: Berkemeier
- first_name: Walter
  full_name: Sextro, Walter
  id: '21220'
  last_name: Sextro
- first_name: Sebastian
  full_name: Peitz, Sebastian
  last_name: Peitz
citation:
  ama: Wohlleben MC, Schütte J, Berkemeier MB, Sextro W, Peitz S. Evaluating Physics-Based,
    Hybrid, and Data-Driven Models for Rubber-Metal Bushings. <i>Multibody System
    Dynamics</i>. Published online 2026:1–21. doi:<a href="https://doi.org/10.1007/s11044-026-10146-9">10.1007/s11044-026-10146-9</a>
  apa: Wohlleben, M. C., Schütte, J., Berkemeier, M. B., Sextro, W., &#38; Peitz,
    S. (2026). Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal
    Bushings. <i>Multibody System Dynamics</i>, 1–21. <a href="https://doi.org/10.1007/s11044-026-10146-9">https://doi.org/10.1007/s11044-026-10146-9</a>
  bibtex: '@article{Wohlleben_Schütte_Berkemeier_Sextro_Peitz_2026, title={Evaluating
    Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings}, DOI={<a
    href="https://doi.org/10.1007/s11044-026-10146-9">10.1007/s11044-026-10146-9</a>},
    journal={Multibody System Dynamics}, author={Wohlleben, Meike Claudia and Schütte,
    Jan and Berkemeier, Manuel Bastian and Sextro, Walter and Peitz, Sebastian}, year={2026},
    pages={1–21} }'
  chicago: Wohlleben, Meike Claudia, Jan Schütte, Manuel Bastian Berkemeier, Walter
    Sextro, and Sebastian Peitz. “Evaluating Physics-Based, Hybrid, and Data-Driven
    Models for Rubber-Metal Bushings.” <i>Multibody System Dynamics</i>, 2026, 1–21.
    <a href="https://doi.org/10.1007/s11044-026-10146-9">https://doi.org/10.1007/s11044-026-10146-9</a>.
  ieee: 'M. C. Wohlleben, J. Schütte, M. B. Berkemeier, W. Sextro, and S. Peitz, “Evaluating
    Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings,” <i>Multibody
    System Dynamics</i>, pp. 1–21, 2026, doi: <a href="https://doi.org/10.1007/s11044-026-10146-9">10.1007/s11044-026-10146-9</a>.'
  mla: Wohlleben, Meike Claudia, et al. “Evaluating Physics-Based, Hybrid, and Data-Driven
    Models for Rubber-Metal Bushings.” <i>Multibody System Dynamics</i>, 2026, pp.
    1–21, doi:<a href="https://doi.org/10.1007/s11044-026-10146-9">10.1007/s11044-026-10146-9</a>.
  short: M.C. Wohlleben, J. Schütte, M.B. Berkemeier, W. Sextro, S. Peitz, Multibody
    System Dynamics (2026) 1–21.
date_created: 2026-01-27T15:51:55Z
date_updated: 2026-03-03T06:31:03Z
department:
- _id: '151'
doi: 10.1007/s11044-026-10146-9
language:
- iso: eng
page: 1–21
publication: Multibody System Dynamics
publication_identifier:
  issn:
  - 1384-5640
quality_controlled: '1'
status: public
title: Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings
type: journal_article
user_id: '43991'
year: '2026'
...
---
_id: '63557'
abstract:
- lang: eng
  text: We discretise a recently proposed new Lagrangian approach to optimal control
    problems with dynamics described by force-controlled Euler-Lagrange equations
    (Konopik et al., in Nonlinearity 38:11, 2025). The resulting discretisations are
    in the form of discrete Lagrangians. We show that the discrete necessary conditions
    for optimality obtained provide variational integrators for the continuous problem,
    akin to Karush-Kuhn-Tucker (KKT) conditions for standard direct approaches. This
    approach paves the way for the use of variational error analysis to derive the
    order of convergence of the resulting numerical schemes for both state and costate
    variables and to apply discrete Noether’s theorem to compute conserved quantities,
    distinguishing itself from existing geometric approaches. We show for a family
    of low-order discretisations that the resulting numerical schemes are ‘doubly-symplectic’,
    meaning they yield forced symplectic integrators for the underlying controlled
    mechanical system and overall symplectic integrators in the state-adjoint space.
    Multi-body dynamics examples are solved numerically using the new approach. In
    addition, the new approach is compared to standard direct approaches in terms
    of computational performance and error convergence. The results highlight the
    advantages of the new approach, namely, better performance and convergence behaviour
    of state and costate variables consistent with variational error analysis and
    automatic preservation of certain first integrals.
author:
- first_name: Michael
  full_name: Konopik, Michael
  last_name: Konopik
- first_name: Sigrid
  full_name: Leyendecker, Sigrid
  last_name: Leyendecker
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  id: '87909'
  last_name: Maslovskaya
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Rodrigo T.
  full_name: Sato Martín de Almagro, Rodrigo T.
  last_name: Sato Martín de Almagro
citation:
  ama: Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martín de Almagro
    RT. On the variational discretisation of optimal control problems for unconstrained
    Lagrangian dynamics. <i>Multibody System Dynamics</i>. Published online 2026.
    doi:<a href="https://doi.org/10.1007/s11044-025-10138-1">10.1007/s11044-025-10138-1</a>
  apa: Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., &#38; Sato Martín de Almagro,
    R. T. (2026). On the variational discretisation of optimal control problems for
    unconstrained Lagrangian dynamics. <i>Multibody System Dynamics</i>. <a href="https://doi.org/10.1007/s11044-025-10138-1">https://doi.org/10.1007/s11044-025-10138-1</a>
  bibtex: '@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_Sato Martín de Almagro_2026,
    title={On the variational discretisation of optimal control problems for unconstrained
    Lagrangian dynamics}, DOI={<a href="https://doi.org/10.1007/s11044-025-10138-1">10.1007/s11044-025-10138-1</a>},
    journal={Multibody System Dynamics}, publisher={Springer Science and Business
    Media LLC}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya,
    Sofya and Ober-Blöbaum, Sina and Sato Martín de Almagro, Rodrigo T.}, year={2026}
    }'
  chicago: Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum,
    and Rodrigo T. Sato Martín de Almagro. “On the Variational Discretisation of Optimal
    Control Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>,
    2026. <a href="https://doi.org/10.1007/s11044-025-10138-1">https://doi.org/10.1007/s11044-025-10138-1</a>.
  ieee: 'M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro,
    “On the variational discretisation of optimal control problems for unconstrained
    Lagrangian dynamics,” <i>Multibody System Dynamics</i>, 2026, doi: <a href="https://doi.org/10.1007/s11044-025-10138-1">10.1007/s11044-025-10138-1</a>.'
  mla: Konopik, Michael, et al. “On the Variational Discretisation of Optimal Control
    Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>,
    Springer Science and Business Media LLC, 2026, doi:<a href="https://doi.org/10.1007/s11044-025-10138-1">10.1007/s11044-025-10138-1</a>.
  short: M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro,
    Multibody System Dynamics (2026).
date_created: 2026-01-12T11:33:54Z
date_updated: 2026-01-12T11:35:27Z
department:
- _id: '636'
doi: 10.1007/s11044-025-10138-1
language:
- iso: eng
publication: Multibody System Dynamics
publication_identifier:
  issn:
  - 1384-5640
  - 1573-272X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On the variational discretisation of optimal control problems for unconstrained
  Lagrangian dynamics
type: journal_article
user_id: '87909'
year: '2026'
...