Abstract
Let’s consider the (very general) example. Consider the motion of a system of N material points.
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Notes
- 1.
Recall that once manifold M is C 1, there is an atlas of class C ∞.
- 2.
Actually we are interested in the tangent bundle TC which is locally described by the generalized coordinates q i and generalized velocities \(\dot {q}^i\).
- 3.
An exact differential form can be reduced to the form df = 0, a gradient form.
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da Costa, N.C.A., Antonio Doria, F. (2022). Lagrangian Formulation. In: On Hilbert's Sixth Problem. Synthese Library, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-030-83837-9_4
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DOI: https://doi.org/10.1007/978-3-030-83837-9_4
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