Lagrangian mechanics on Lie groups: a pedagogical approach

2011/11/05 by Andrew Lucas, A. Lucas, Lucas, A.
Engineering · Mathematics · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Geophysics and Sensor Technology #Geotechnical and Geomechanical Engineering #Mathematical Physics (math-ph) #Particle Accelerators and Free-Electron Lasers #math-ph #math.MP #physics.class-ph

paper · pdf · doi:10.48550/arxiv.1111.1275

12 pages

arxiv created 2011/11/05 · openalex publication_date 2011/11/05 · arxiv updated 2011/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a new method to formulate classical Lagrangian mechanics on a finite-dimensional Lie group. This new approach is much more pedagogical than many previous treatments of the subject, and it directly introduces students to generator matrices and their usefulness in many manipulations. The example of rigid body rotation, i.e. motion on the Lie group SO(3), is used as an example, and it is shown how to derive Euler's equations directly from the principle of least action. The techniques covered in this paper generalize to other Lie groups in a straightforward manner, which is discussed. We briefly discuss the Hamiltonian formulation of the problem as well.

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