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REVIEW 4 major objections 5 minor 53 references

Impacts between multibody systems and deformable structures

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read When a multibody system strikes an elastic structure, standard rigid impact models become impractical and soft-contact models give rebound counts that depend on the arbitrarily chosen contact stiffness.

desk verdict A careful but narrow numerical case study of multi-contact impacts with elastic supports; the standard methods are clearly presented, but the broad conclusions in Section 8 overreach what the undamped three-mass simulations actually support. read the letter →

arxiv 2506.10034 v1 pith:ORJKUKVO submitted 2025-06-10 physics.class-ph cs.ROcs.SYeess.SY

Lipinski Krzysztof This is my paper · ORCID
classification physics.class-phcs.ROcs.SYeess.SY MSC 70E5570F35 PACS 45.40.-f
keywords impactmodellingmultibodydynamicsunilateralconstraintssoftcontactmodelsdeformablestructuresimpulse-momentumbalancebrachiationrobotselasticcollisions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tackles a practical modeling problem: a multibody mechanism, motivated by brachiation robots swinging between branches, collides with an elastic structure such as a vibrating cable, and the collision turns into a train of rebounds rather than one clean impact. The author argues that the two standard approaches both fail here: classical rigid-body impulse-momentum balance requires stopping and restarting the numerical integration at every rebound, which quickly becomes impractical, and soft-contact models yield a count of rebounds that depends strongly on the chosen contact spring stiffness, even though the gross motion of the multibody part is nearly unaffected. The duration of the contact episode instead tracks the slowest vibration frequency of the elastic counterpart. If this is right, engineers modeling impacts on flexible structures should not trust either idealization, and simulation effort should go into resolving the low-frequency vibration of the target structure rather than fine-tuning the contact law.

What carries the argument

The load-bearing object is a lumped three-mass chain connected by springs, used as the deformable reference, with the contact itself modeled as a unilateral linear spring that transmits only compressive forces and has no damping; the multibody side is formulated in joint coordinates with Newton/Euler dynamics, and impact impulses are mapped to joint-velocity changes through the mass matrix and a contact-point Jacobian in equations (5)-(12). By varying the unilateral spring's stiffness and the chain masses, the model generates the multi-rebound sequences and shows that contact duration is set by the chain's slowest vibration mode rather than by the contact stiffness. A second, simpler system with two rigid bodies and three unilateral contact points demonstrates why impulse-momentum balancing becomes ambiguous when several unilateral constraints are active at once.

What would settle it

Perform an instrumented collision between a rigid arm and a real cable or beam, varying either the contact stiffness at the gripper or the structural damping, and count the distinct rebounds and measure the total contact duration; the paper's claim fails if contact duration does not track the slowest vibration frequency, if rebound count does not grow with contact stiffness, or if modest damping removes the multi-rebound sequence.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that impacts with deformable structures are inherently multi-event. In numerical experiments with a three-mass undamped spring chain as the elastic target and a unilateral spring at the contact, the colliding arm shows up to nine rebounds during one contact episode, with the rebound count rising as contact stiffness is increased by factors of 2, 4, 10, and 100 over the reference value, while the total in-touch time stays nearly the same and mainly matches the slowest frequency of the elastic counterpart. The overall motion of the multibody part, such as the arm endpoint displacement and the velocity of the main body, is only weakly dependent on the assumed contact stiffness. From these observations the paper concludes that classic unilateral constraint models and impact-momentum balance techniques are impractical for such cases, and soft-contact models are problematic because their rebound counts are parameter-sensitive.

Load-bearing premise

The argument relies on the undamped three-mass spring chain with a unilateral linear spring being a faithful enough model of a real flexible cable or branch; in a real structure, energy dissipation could change both the number and timing of rebounds.

Editorial extensions

If this is right

  • Designers of brachiation or cable-inspection robots should expect a collision with a flexible cable to produce several rebounds, not one clean impact event.
  • Simulation algorithms based on rigid impact events will need one stop-and-restart per rebound, making them costly or impractical when the target is elastic.
  • Soft-contact simulations should treat rebound count as a parameter-sensitive output, not a reliable prediction; the stable outputs are total contact duration and gross multibody motion.
  • Contact duration can be predicted from the slowest vibration frequency of the elastic counterpart, offering a cheaper modeling target than the local contact law.
  • Larger contact stiffness mainly increases the number of rebounds, so increasing stiffness in a soft-contact model does not make the impact more accurate in terms of overall motion.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Untested by the paper: adding even mild damping to the chain would likely reduce the rebound count, so the many-rebound prediction may overstate what happens with real cables, which dissipate energy.
  • If the global-motion insensitivity holds, grasp-timing control could ignore uncertain contact stiffness and rely on a low-order model of the structure's slowest mode.
  • Impulse-momentum methods might be rescued by merging closely spaced rebounds into one effective impact with an energy-based restitution coefficient, avoiding repeated event stops.
  • The contact-duration/frequency relation suggests that measuring a structure's fundamental mode from a free-vibration test could calibrate impact timing without resolving the detailed contact force law.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies impact modeling in multibody systems colliding with deformable structures, with brachiating robots as the motivating application. The first part (Sections 3-4) derives standard impulse-momentum balance equations for frictionless and frictional impacts, expressing post-impact velocity changes in terms of the mass matrix, constraint Jacobians, and a restitution coefficient. The second part presents two numerical studies: a ten-body planar manipulator hitting a rigid obstacle, and a planar system with three unilateral contacts where the endpoint hits a three-mass elastic chain with unilateral springs. The main conclusions, stated in Section 8, claim that classical impact-momentum balance techniques are impractical for impacts with elastic structures because multiple rebounds require repeated interruption of integration, and that soft-contact models are problematic because rebound counts depend on contact stiffness while the total contact duration tracks the slowest vibration frequency of the elastic counterpart.

Significance. The paper's main contributions are the standard rigid-impact formulation with frictional cases and two illustrative numerical examples. The observation in Section 6 that the ratio of elasticities at distant contact points is a significant model parameter is interesting and worth reporting. However, the broad conclusions in Section 8 about the impracticality of rigid methods and the problematic nature of soft-contact models are not supported by the numerical evidence presented. The claims are based entirely on an undamped, three-mass lumped-parameter model without validation, convergence studies, or comparison with state-of-the-art nonsmooth solvers. If the conclusions were supported, they would be useful guidance for modeling brachiation robot interactions with flexible cables; as it stands, the paper does not establish them. The rigid-impact derivation is standard and appears correct, but it is not the load-bearing new content.

major comments (4)
  1. [Section 7 and Section 8] The central conclusion that soft-contact models are 'problematic' and that contact duration corresponds mainly to the slowest vibration frequency rests solely on the three-mass undamped spring chain described in Section 7 (Fig. 4d), where 'all springs are free of damping/dissipation of the energy.' In an undamped linear chain with a unilateral spring, repeated re-contact is an expected mathematical consequence: after separation, the masses vibrate with undiminished amplitude, and re-contact occurs when the end displacement returns to zero. Real flexible cables and branches possess material and aerodynamic damping and are distributed-parameter systems. Without sensitivity studies with damping or comparison against a beam or cable model, the claim that rebound counts are sensitive to contact stiffness in a way that is problematic is not established for the systems that the paper ultimately targets (brachiating robots grasping vibrating cables). This is a load-bearing issue for the paper's main conclusion.
  2. [Section 8] The statement that classical unilateral constraint models and impact-momentum balance techniques are 'impractical' because each rebound demands stopping the numerical integration is an implementational critique of a naive event-driven scheme. Complementarity-based nonsmooth solvers, such as those of Moreau and Glocker-Pfeiffer (references [13], [28], and [29] in the paper), handle multiple simultaneous or successive impacts within a single time step without stopping the integration. The paper does not compare its event-driven approach with such methods, so the broad claim of impracticality is an opinion rather than a result established by the manuscript's own analysis. This is load-bearing for the recommendation against rigid methods.
  3. [Sections 6-7] The numerical studies lack validation, convergence analysis, and error bounds. The only numerical details given are the use of MATLAB's ODE45 with maximal and initial time steps of 10^-4 s and relative/absolute tolerances of 10^-4 and 10^-6. There is no mesh-convergence study, no benchmark against an analytical or high-fidelity solution, and no assessment of how the discrete rebound counts shown in Fig. 8 depend on the integration tolerances or time steps. Since the paper reports a specific number of rebounds (up to 9) and claims that the total contact duration is nearly independent of stiffness, convergence evidence is necessary to distinguish physical behavior from numerical artifacts.
  4. [Section 6] The soft-contact model used in Section 6 is not fully specified. The paper refers to a 'smoothed contact model (elastic contact area)' but does not give the constitutive relation for the contact force (e.g., linear spring, Hertzian, with or without damping), the exact definition of penetration, or how the unilateral constraints at points A, B, and C are enforced and smoothed. The parameters c1A, c2A, c3A are stated, but the functional form of the contact force is absent. This makes the numerical results irreproducible and prevents the reader from assessing whether the observed behaviors are artifacts of the particular regularization.
minor comments (5)
  1. [Section 3] There are two equations labeled (5): the modified dynamic equation and its integrated form; subsequent equation numbers (6)-(12) are shifted accordingly. This numbering error makes the derivation harder to follow.
  2. [Section 4] The text in Eq. (13) says 'Eqs. (13) contain four unknown' but only two equations are displayed; the logical flow of the case distinction for slip and stick is dense and would benefit from a table or explicit step-by-step summary.
  3. [Section 7] Fig. 8 caption uses c14 in some labels while the text uses cref for the reference stiffness; the caption also does not directly state which subfigure corresponds to which stiffness ratio, and the claimed rebound counts (e.g., 9 rebounds) are not evident from the plotted curves. A table listing stiffness, number of rebounds, and total contact duration would greatly improve clarity.
  4. [Throughout] There are several typographical errors that should be corrected: 'locomoion' in the Fig. 1 caption, 'Culomb' in Section 4, 'vetrices' in Section 2, and the moment of inertia for body #4 is consistently labeled I3 instead of I4 in Section 6.
  5. [Section 8] The claim that 'the overall motion of the multibody part appears to be not influenced (or slightly influenced) by assumed values of the connecting elasticity' is presented without quantitative support; providing a plot of, for example, the arm's final angle or velocity versus c13 would make the claim verifiable.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the numerical results are direct simulations of explicitly stated models with user-chosen stiffness, restitution, and friction parameters; the conclusions do not reduce by construction to a fitted quantity or to a self-citation chain.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The impulse-momentum equations in Sections 3 and 4, e.g., eqs. (6) and (10)-(12), are algebraic consequences of integrating eq. (5) under the stated assumptions of infinitesimal impact duration and constant configuration; the restitution coefficient R and friction coefficient mu are inputs, not fitted outputs. The Section 6 and Section 7 simulations integrate the assumed ODEs with prescribed elasticities and masses, and the observed quantities - penetration histories, rebound counts, and contact durations - are outputs of those integrations. In particular, the multi-rebound behavior is explicitly tied to an undamped model: 'All springs are free of damping/dissipation of the energy (we intend to investigate a purely elastic impact).' Whether that undamped three-mass chain adequately represents a real flexible cable is a modeling-assumption concern, not a circularity. The self-citations [9], [50], and [52] provide the multibody formalism and earlier impact equations, but those equations are standard impulse-momentum balance relations and are not used to assume the paper's conclusions about soft-contact rebound counts or the relation between contact duration and the slowest vibration frequency. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and no result reduces by definition to its own input. The broad claims in Section 8 about the impracticality of rigid impact methods and the problematic nature of soft-contact models are interpretations of a deliberately idealized simulation, not circularly forced conclusions. Accordingly, no specific circular step can be quoted and exhibited, and the circularity burden is minimal.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper contributes numerical experiments; it does not introduce new physical entities. The key inputs are user-chosen stiffnesses and masses, and the core observations follow from the assumed linear undamped spring models. No external benchmarks or fitted parameters are used, so circularity is low.

free parameters (5)
  • Restitution coefficient R = not stated
    Used in eq. (11) and in Section 5 examples, but its numerical value is never given, so the rigid-impact results are not fully determined.
  • Friction coefficient mu = 0, 0.15, 0.35
    Chosen by hand in Section 5 to demonstrate friction effects; the Coulomb model itself is flagged as disputable.
  • Contact spring stiffness at point A, cA = 1e6, 4e6, 16e6 N/m
    Stiffness at contact point A varied in Section 6 to study the ratio with contact C; the ratio is called a 'significant model parameter'.
  • Unilateral spring stiffness c13 = 2, 4, 10, 100 x 1.6e5 N/m
    Stiffness of the unilateral spring varied in Section 7; the main focus of the paper. Determines number of rebounds.
  • Mass of elastic counterpart m13 = 0.1, 1.2, 3.2 kg
    Mass of the elastic counterpart varied in Section 7 to identify three rebound regimes.
assumptions (5)
  • standard math Newton-Euler dynamics and joint-coordinate kinematics for tree-like multibody systems
    Section 2 builds the equations of motion (4) using the formulation in refs [50-52]; the central simulations rest on these equations.
  • standard math Impulse-momentum balance equations (10)-(12) and (14)-(18)
    Sections 3-4 take the rigid-impact equations directly from refs [6,9,14,50]; the numerical examples in Section 5 apply them.
  • domain assumption Coulomb friction is applicable during impact
    Section 4 says 'we have supposed that the classical model of Coulomb is applicable for impact forces. It is disputable.' This affects all frictional results in Section 5.
  • domain assumption Contact forces are represented by linear unilateral springs with no damping
    Sections 6-7 use spring contact models; the absence of damping and the linear force-penetration law drive the rebound counts and contact durations.
  • domain assumption The three-mass spring chain adequately represents a deformable reference body
    Section 7 and Fig. 4d model the elastic counterpart as 3 masses and springs; the conclusions about in-touch duration and rebound numbers depend on this lumped representation.

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Cite this review

Pith. "Pith review of Impacts between multibody systems and deformable structures." pith.science (2026). https://pith.science/paper/ORJKUKVO

@misc{pith2026250610034,
  author       = {Pith},
  title        = {Pith review of: Impacts between multibody systems and deformable structures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ORJKUKVO}},
  note         = {Machine review of arXiv:2506.10034}
}
read the original abstract

Collisions and impacts are the principal reasons for impulsive motions, which we frequently see in dynamic responses of systems. Precise modelling of impacts is a challenging problem due to the lack of the accurate and commonly accepted constitutive law that governs their mechanics. Rigid-body approach and soft contact methods are discussed in this paper and examined in the presented numerical examples. The main focus is set to impacts in systems with multiple unilateral contacts and collisions with elastic elements of the reference. Parameters of interconnecting unilateral springs are under discussion.

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Works this paper leans on

53 extracted references · 50 canonical work pages

  1. [13]

    In: Multibody dynamics 2007, conference proceedings, pp

    Tasora, A.: High Performance Complementarity Solver for Non-Smooth Dynamics. In: Multibody dynamics 2007, conference proceedings, pp. [1–20], June 25–28, Milan, Italy (2007)

    work page 2007

  2. [28]

    Nonlinear Dyn

    Glocker, Ch., Pfeiffer, F.G.: Multiple impact with friction in rigid multibody systems. Nonlinear Dyn. 7, 471–491 (1995). https://doi.org/10.1007/BF00121109

    work page doi:10.1007/bf00121109 1995

  3. [29]

    Wiley, New York, 1996

    Pfeiffer, F.G., Glocker, Ch.: Multibody Dynamics with Unilateral Contacts. Wiley, New York, 1996

    work page 1996

  4. [1]

    Robotica

    Andreuchetti, S., Oliveira, V., Fukuda, T.: A Survey on Brachiation Robots: An Energy-Based Review. Robotica. 39, 1588–1600 (2021). doi:10.1017/S026357472000137X

    work page doi:10.1017/s026357472000137x 2021

  5. [2]

    In: Proceedings of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain, 1–5 October 2018, pp

    Davies, E., Garlow, A., Farzan, S., Rogers, J., Hu, A.-P.: Tarzan: Design, Prototyping, and Testing of a Wire-Borne Brachiating Robot. In: Proceedings of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain, 1–5 October 2018, pp. 7609–7614 (2018). https://doi.org/10.1109/IROS.2018.8593823

    work page arXiv 2018

  6. [3]

    Lin, C.-Y., Tian, Y.-J.: Design of Transverse Brachiation Robot and Motion Control System for Locomotion between Ledges at Different Elevations. Sensors. 22, 4031- (2022). https://doi.org/10.3390/s22114031

    work page doi:10.3390/s22114031 2022

  7. [4]

    Lo, A.K.-Y., Yang, Y.-H., Lin, T.-C., Chu, C.-W., Lin, P.-C.: Model-Based Design and Evaluation of a Brachiating Monkey Robot with an Active Waist. Appl. Sci. 7, 947- (2017). https://doi.org/10.3390/app7090947

    work page doi:10.3390/app7090947 2017

  8. [5]

    Lipinski, K.: Closed Form Constraint Equations Used to Express Frictionless Slip of Multibody Systems Attached to Finite Elements - Application to a Contact between a Double Pendulum and a Beam. Appl. Sci. 13, 3681- (2023). https://doi.org/10.3390/app13063681

    work page doi:10.3390/app13063681 2023

Show all 53 references
  1. [6]

    G.: Applications of unilateral multibody dynamics

    Pfeiffer, F. G.: Applications of unilateral multibody dynamics. Phil. Trans. R. Soc. Lond. A. 359, 2609–2628 (2001). https://doi.org/10.1098/rsta.2001.0912 18

    2001

  2. [7]

    Kovecses, J., Cleghorn, W.L.: Finite and impulsive motion of constrained mechanical systems via Jourdain’s principle: discrete and hybrid parameter models. Int. J. Non-Linear Mech., 38, 935– 956 (2003). https://doi.org/10.1016/S0020-7462(02)00039-2

    2003 doi

  3. [8]

    Multibody Syst Dyn

    Vukobratovic, M., Potkonjak, V., Babkovic, K., Borovac, B.: Simulation model of general human and humanoid motion. Multibody Syst Dyn. 17, 71–96 (2007). https://doi.org/10.1007/s11044-006-9034-2

    2007 doi

  4. [9]

    In: The 5th Joint International Conference on Multibody System Dynamics, Liznona: IDMEC - Instituto Superior Técnico, University of Lisbon, pp.1-17 (2108)

    Lipiński K.: Impacts in case of triple unilaterally constrained system. In: The 5th Joint International Conference on Multibody System Dynamics, Liznona: IDMEC - Instituto Superior Técnico, University of Lisbon, pp.1-17 (2108)

  5. [10]

    A.: Modeling of Impact in Multibody Systems: An Overview

    Khulief, Y. A.: Modeling of Impact in Multibody Systems: An Overview. ASME. J. Comput. Nonlinear Dynam. 8(2), 021012 (2013). https://doi.org/10.1115/1.4006202

    2013 doi

  6. [11]

    In: Multibody dynamics 2007, conference proceedings, pp

    Lutz, A.: Simulation of Numerous Contacts in an Industrial Educational System Using an Augmented Lagrangian Approach. In: Multibody dynamics 2007, conference proceedings, pp. [1– 12], June 25–28, Milan, Italy (2007)

    2007

  7. [12]

    G.: CVT - A Large Application of Nonsmooth Mechanics

    Pfeiffer, F. G.: CVT - A Large Application of Nonsmooth Mechanics. In: Multibody dynamics 2007, conference proceedings, pp. [1–20], June 25–28, Milan, Italy (2007)

    2007

  8. [14]

    In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, pp

    Müller, A.: Forward Dynamics of Variable Topology Mechanisms –The Case of Constraint Activation. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, pp. 184–195, June 29–July 2, Barcelona, Spain (2015)

    2015

  9. [15]

    Chang, C.C., Huston, R.L.: Computational methods for studying impact in multibody systems. Comput. & Structures.57,421–425(1995). https://doi.org/10.1016/0045-7949(94)00631-C

    1995 doi

  10. [16]

    Multibody Syst Dyn

    Chang, C.C., Liu, C.Q., Huston, R.L.: Dynamics of Multibody Systems Subjected to Impulsive Constraints. Multibody Syst Dyn. 8, 161–184 (2002). https://doi.org/10.1023/A:1019537611060

    2002 doi

  11. [17]

    Multibody Syst Dyn

    Chang C.C., Peng, S-T.: Impulsive motion of multibody systems. Multibody Syst Dyn. 17, 47–70 (2007). https://doi.org/10.1007/s11044-007-9035-9

    2007 doi

  12. [18]

    Teubner, Stuttgart (1977)

    Wittenburg, J.: Dynamics of system of rigid bodies, B.G. Teubner, Stuttgart (1977)

    1977

  13. [19]

    Trends in applications of pure mathematics to mechanics, 2, 263–280 (1979)

    Moreau, J.J.: Application of convex analysis to some problems of dry friction. Trends in applications of pure mathematics to mechanics, 2, 263–280 (1979)

    1979

  14. [20]

    Non-smooth Mechanics and Applications

    Moreau, J.J.: Unilateral contact and dry friction in finite freedom dynamics. Non-smooth Mechanics and Applications. CISM Courses and Lectures. 302, Springer, (1988)

    1988

  15. [21]

    Birkhauser (1985)

    Panagiotopoulos, P.D.: Inequality problems in mechanics and applications. Birkhauser (1985)

    1985

  16. [22]

    D.: Hemivariational inequalities

    Panagiotopoulos, P. D.: Hemivariational inequalities. Springer (1993)

    1993

  17. [23]

    Haug, E.J., Wu, S.C., Yang, S.M.: Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition–deletion–Part I: Theory. Mech. Mach. Theory. 21(5), 401– 406 (1986). https://doi.org/10.1016/0094-114X(86)90088-1

    1986 doi

  18. [24]

    Khulief, Y.A., Shabana, A.A.: Impact response of multi-body systems with consistent and lumped masses. J. Sound Vibration. 104(2), 187–207 (1986). https://doi.org/10.1016/0022- 460X(86)90263-4 19

    1986 doi

  19. [25]

    Rismantab-Sany, J., Shabana, A.A.: Impulsive motion of non-holonomic deformable multibody systems, Parts I and II. J. Sound Vibration. 127, 193–219 (1988). https://doi.org/10.1016/0022-460X(88)90296-9

    1988 doi

  20. [26]

    Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Design, 112(3), 369–376 (1990). https://doi.org/10.1115/1.2912617

    1990 doi

  21. [27]

    Lankarani, H.M., Nikravesh, P.E.: Canonical impulse-momentum equations for impact analysis of multibody systems. J. Mech. Des., 114(1), 180–186 (1992). https://doi.org/10.1115/1.2916914

    1992 doi

  22. [30]

    Paper No

    Zakhariev, E.V.: A numerical method for multibody system frictional impact simulation. Paper No. DETC2001/VIB-21367, In: Proc of ASME 2001 DETC, Pittsburgh PA. (2001)

    2001

  23. [31]

    In: Visual Nonlinear Multibody Systems

    Zakhariev, E.V.: Multibody system contact dynamics simulation. In: Visual Nonlinear Multibody Systems. Kluwer Academic Publishers, Dordrecht, The Netherlands, 383–402 (2003)

    2003

  24. [32]

    In: IUTAM Symposium on Multiscale Problems in Multibody System Contacts, pp

    Ebrahimi, S., Eberhard, P.: Frictional Impact of Planar Deformable Bodies. In: IUTAM Symposium on Multiscale Problems in Multibody System Contacts, pp. 23-32, February 20-23, Stuttgart, Germany (2007)

    2007

  25. [33]

    In: Proceedings of the 2nd ECMI Workshop o Numerical methods in Multibody Dynamics (2006)

    Ebrahimi, S., Eberhard, P.: A linear complementarity formulation on position level for frictionless impact of planar deformable bodies. In: Proceedings of the 2nd ECMI Workshop o Numerical methods in Multibody Dynamics (2006)

    2006

  26. [34]

    Stronge, W.J.: Generalized impulse and momentum applied to multibody impact with friction. Mech. Struct. Mach. 29, 239–260 (2001). https://doi.org/10.1081/SME-100104482

    2001 doi

  27. [35]

    In: Visual Nonlinear Multibody Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp

    Ambrosio, J.A.C.: Impact of rigid and flexible multibody systems: deformation description and contact models. In: Visual Nonlinear Multibody Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 57–81, (2003)

    2003

  28. [36]

    In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, pp

    Chadaj, K., Malczyk, P., Fraczek, J.: Parallel recursive Hamiltonian formulation for constrained multibody system dynamics. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, pp. 217–228, June 29–July 2, Barcelona, Spain (2015)

    2015

  29. [37]

    In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, pp

    Schreyer, F., Leine, R.I.: A mixed shooting and harmonic balance method for mechanical systems with dry friction or other local nonlinearities. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, pp. 491–501, June 29–July 2, Barcelona, Spain (2015)

    2015

  30. [38]

    In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015 , pp

    Dupac, M.: Spatial Impact of a Beam Attached to a Sliding Structure. In: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015 , pp. 577–584, June 29–July 2, Barcelona, Spain (2015)

    2015

  31. [39]

    In: Proceedings of the 8th ECCOMAS Thematic Conference on Multibody Dynamics 2017 , pp

    Jankowski, K.P., Chaudhry, S., Czekanski, A.: Selection and Experimental Validation of Contact / Impact Models Suitable for Multibody Dynamics Simulations. In: Proceedings of the 8th ECCOMAS Thematic Conference on Multibody Dynamics 2017 , pp. 309-314, June 19 – 22, Prague, Cz...

    2017

  32. [40]

    In: Proceedings of the 8th ECCOMAS Thematic Conference on Multibody Dynamics 2017 , pp

    Tschigg, S., Seifried, R.: Efficient Evaluation of Local and Global Deformations in Impact Simulations in Reduced Flexible Multibody Systems based on a Quasi-Static Contact Submodel. In: Proceedings of the 8th ECCOMAS Thematic Conference on Multibody Dynamics 2017 , pp. 315-32...

    2017

  33. [41]

    In: Proceedings of the ECCOMAS Thematic Conference in Multibody Dynamics, June 25–28, Milan, Italy (2007)

    Allotta, B., Pugi, L., Bartolini, F.: Design and development of a railway pantograph with a wire-pulley transmission system. In: Proceedings of the ECCOMAS Thematic Conference in Multibody Dynamics, June 25–28, Milan, Italy (2007)

    2007

  34. [42]

    Ambrosio, J., Pombo, J., Pereira, M., Antunes, P., Mosca, A.: A Computational procedure for the dynamic analysis of the Catenary-pantograph interaction in High-speed trains. J. Theor. Appl. Mech. 50, 681–699 (2012)

    2012

  35. [43]

    Antuanes, P., Ambrosio, J., Pombo, J., Facchinetti, A.: A new methodology to study the pantograph-catenary dynamics in curved railway tracks. Veh. Syst. Dyn. 58, 425–452 (2019) https://doi.org/10.1080/00423114.2019.1583348

    2019

  36. [44]

    Multibody Syst

    Qian, Z., Zhang, D., Jin, C.: A regularized approach for frictional impact dynamics of flexible multi-link manipulator arms considering the dynamic stiffening effect. Multibody Syst. Dyn. 43, 229–255 (2018). https://doi.org/10.1007/s11044-017-9589-0

    2018 doi

  37. [45]

    Multibody Syst

    Tang, L., Liu, J.: Frictional contact analysis of sliding joints with clearances between flexible beams and rigid holes in flexible multibody systems. Multibody Syst. Dyn. 49, 155 –179 (2020). https://doi.org/10.1007/s11044-019-09717-w

    2020 doi

  38. [46]

    In: Proceedings of the ACMD’02, The First Asian Conference on Multibody Dynamics 2002, Iwaki, Japan, July 31–2 August (2002)

    Schwab, A.L., Meijaard, J.P.: Two Special Finite Elements for Modeling Rolling Contact in a Multibody Environment. In: Proceedings of the ACMD’02, The First Asian Conference on Multibody Dynamics 2002, Iwaki, Japan, July 31–2 August (2002)

    2002

  39. [47]

    Multibody Syst

    Antunes, P., Magalhaes, H., Ambrósio, J., Pombo, J., Costa, J.: A co-simulation approach to the wheel–rail contact with flexible railway track. Multibody Syst. Dyn. 45, 245 –272 (2019). https://doi.org/10.1007/s11044-018-09646-0

    2019 doi

  40. [48]

    Skrinjar, L., Slavic, J., Boltezar, M.: A review of continuous contact-force models in multibody dynamics. Int. J. Mech. Sci. 145, 171–187 (2018). https://doi.org/10.1016/j.ijmecsci.2018.07.010

    2018 doi

  41. [49]

    Multi-body contact in non-linear dynamics of real mechanical systems

    Atanasovska, I. Multi-body contact in non-linear dynamics of real mechanical systems. Procedia Eng. 199, 510–515 (2017). https://doi.org/10.1016/j.proeng.2017.09.139

    2017 doi

  42. [50]

    Wydawnictwo Politechniki Gdańskiej, Seria Monografie 123, Gdańsk (2012) (in Polish)

    Lipinski, K.: Multibody Systems with Unilateral Constraints in Application to Model Complex Mechanical Systems. Wydawnictwo Politechniki Gdańskiej, Seria Monografie 123, Gdańsk (2012) (in Polish)

    2012

  43. [51]

    Fisette, P., Samin, J.C.: Symbolic Modeling of Multibody System, Kluwer Acad. Pub. (2003)

    2003

  44. [52]

    Multibody Syst Dyn

    Docquier, N., Lipinski, K., Lantsoght, O., Timmermans S., Fisette P.: Symbolic multibody models for digital-twin applications. Multibody Syst Dyn. 62, 137–163 (2024). https://doi.org/10.1007/s11044-023-09957-x

    2024 doi

  45. [53]

    http://www.mathworks.com

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.