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Hamel's Equations From d'Alembert's Principle and Frame Kinematics.

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Title: Hamel's Equations From d'Alembert's Principle and Frame Kinematics.
Authors: Wensing, Patrick M.1
Source: Journal of Applied Mechanics. Aug2026, Vol. 93 Issue 8, p1-3. 3p.
Subjects: Frames (Vector analysis), Kinematics, Virtual work, Symbolic computation, Engineering systems, Lie algebras, Equations of motion, Nonholonomic dynamical systems
Abstract: Hamel's equations express the equations of motion of a mechanical system using generalized speeds associated with a configuration-dependent frame. These equations are classical and well established, with existing derivations commonly either starting from the Euler-Lagrange equations in coordinates or invoking additional variational constructions (i.e., transitivity equations). Although correct, these approaches can obscure the kinematic origin of the terms arising from noncoordinate frames. This technical brief presents a concise alternative derivation of Hamel's equations that applies d'Alembert's principle directly in terms of generalized speeds and relies on a kinematic identity involving the Lie bracket of the frame vector fields. This development isolates the role of frame noncommutativity without introducing auxiliary variational machinery. The final equations are amenable to modern symbolic modeling workflows, where automatic differentiation can be used to evaluate the contributions from frame noncommutativity without precomputing structure coefficients. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mechanics is the property of American Society of Mechanical Engineers 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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DbLabel: Engineering Source
An: 196911138
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PubType: Academic Journal
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  Data: Hamel's Equations From d'Alembert's Principle and Frame Kinematics.
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  Data: Hamel's equations express the equations of motion of a mechanical system using generalized speeds associated with a configuration-dependent frame. These equations are classical and well established, with existing derivations commonly either starting from the Euler-Lagrange equations in coordinates or invoking additional variational constructions (i.e., transitivity equations). Although correct, these approaches can obscure the kinematic origin of the terms arising from noncoordinate frames. This technical brief presents a concise alternative derivation of Hamel's equations that applies d'Alembert's principle directly in terms of generalized speeds and relies on a kinematic identity involving the Lie bracket of the frame vector fields. This development isolates the role of frame noncommutativity without introducing auxiliary variational machinery. The final equations are amenable to modern symbolic modeling workflows, where automatic differentiation can be used to evaluate the contributions from frame noncommutativity without precomputing structure coefficients. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Applied Mechanics is the property of American Society of Mechanical Engineers 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: 10.1115/1.4072299
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      – Code: eng
        Text: English
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        PageCount: 3
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      – SubjectFull: Frames (Vector analysis)
        Type: general
      – SubjectFull: Kinematics
        Type: general
      – SubjectFull: Virtual work
        Type: general
      – SubjectFull: Symbolic computation
        Type: general
      – SubjectFull: Engineering systems
        Type: general
      – SubjectFull: Lie algebras
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      – SubjectFull: Equations of motion
        Type: general
      – SubjectFull: Nonholonomic dynamical systems
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      – TitleFull: Hamel's Equations From d'Alembert's Principle and Frame Kinematics.
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              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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