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Conserving integration of multibody systems with singular and non-constant mass matrix including quaternion-based rigid body dynamics.

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Title: Conserving integration of multibody systems with singular and non-constant mass matrix including quaternion-based rigid body dynamics.
Authors: Kinon, Philipp L.1 (AUTHOR) philipp.kinon@kit.edu, Betsch, Peter1 (AUTHOR) peter.betsch@kit.edu
Source: Multibody System Dynamics. Feb2025, Vol. 63 Issue 1, p303-340. 38p.
Subjects: Rigid body mechanics, Holonomic constraints, Equations of motion, Rigid bodies, Euler method
Abstract: Mechanical systems with singular and/or configuration-dependent mass matrix can pose difficulties to Hamiltonian formulations, which are the standard choice for the design of energy-momentum conserving time integrators. In this work, we derive a structure-preserving time integrator for constrained mechanical systems based on a mixed variational approach. Livens' principle (or sometimes called Hamilton–Pontryagin principle) features independent velocity and momentum quantities and circumvents the need to invert the mass matrix. In particular, we take up the description of rigid body rotations using unit quaternions. Using Livens' principle, a new and comparatively easy approach to the simulation of these problems is presented. The equations of motion are approximated by using (partitioned) midpoint discrete gradients, thus generating a new energy-momentum conserving integration scheme for mechanical systems with singular and/or configuration-dependent mass matrix. The derived method is second-order accurate and algorithmically preserves a generalized energy function as well as the holonomic constraints and momentum maps corresponding to symmetries of the system. We study the numerical performance of the newly devised scheme in representative examples for multibody and rigid body dynamics. [ABSTRACT FROM AUTHOR]
Copyright of Multibody System Dynamics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Conserving integration of multibody systems with singular and non-constant mass matrix including quaternion-based rigid body dynamics.
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  Data: <searchLink fieldCode="DE" term="%22Rigid+body+mechanics%22">Rigid body mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Holonomic+constraints%22">Holonomic constraints</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+of+motion%22">Equations of motion</searchLink><br /><searchLink fieldCode="DE" term="%22Rigid+bodies%22">Rigid bodies</searchLink><br /><searchLink fieldCode="DE" term="%22Euler+method%22">Euler method</searchLink>
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  Data: Mechanical systems with singular and/or configuration-dependent mass matrix can pose difficulties to Hamiltonian formulations, which are the standard choice for the design of energy-momentum conserving time integrators. In this work, we derive a structure-preserving time integrator for constrained mechanical systems based on a mixed variational approach. Livens' principle (or sometimes called Hamilton–Pontryagin principle) features independent velocity and momentum quantities and circumvents the need to invert the mass matrix. In particular, we take up the description of rigid body rotations using unit quaternions. Using Livens' principle, a new and comparatively easy approach to the simulation of these problems is presented. The equations of motion are approximated by using (partitioned) midpoint discrete gradients, thus generating a new energy-momentum conserving integration scheme for mechanical systems with singular and/or configuration-dependent mass matrix. The derived method is second-order accurate and algorithmically preserves a generalized energy function as well as the holonomic constraints and momentum maps corresponding to symmetries of the system. We study the numerical performance of the newly devised scheme in representative examples for multibody and rigid body dynamics. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Multibody System Dynamics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s11044-024-10001-9
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        Text: English
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      – SubjectFull: Rigid body mechanics
        Type: general
      – SubjectFull: Holonomic constraints
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      – SubjectFull: Equations of motion
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      – SubjectFull: Rigid bodies
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              Text: Feb2025
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