Abstract
Starting from a smooth manifold Q as configurational space, the intrinsec form of Euler–Lagrange equation is derived using a differential geometrical approach in order to obtain a relation valid on the whole tangent bundle TQ that constitutes the phase space of a generical mechanical system.
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Grimaldi, P. Global methods in classical mechanics. The Euler–Lagrange equation. Journal of Mathematical Chemistry 24, 71–78 (1998). https://doi.org/10.1023/A:1019110400670
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DOI: https://doi.org/10.1023/A:1019110400670