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What is Coordinate-Free Euler-Lagrange Derivation about?

The document presents a coordinate-free derivation of the Euler–Lagrange equations for C2-minimizing curves on manifolds, demonstrating that the derivation is independent of vector field extensions and does not impose additional differentiability constraints. It also characterizes minimizing curves based on their local behavior, establishing that if a curve is minimizing, any sub-arc is also minimizing. The findings are significant for understanding the nature of minimization problems in a coordinate-indepe

Author

soamoxsugamuxi

Language

EN