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. |
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| 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] |
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| Database: | Engineering Source |
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