2-4: Nonlinear Finite Elements in 1-D (Total Lagrangian vs. Updated Lagrangian)

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Develops the idea of motion as a mapping of material points to current locations in space. Defines displacement and velocity. Defines total Lagrangian vs. Updated Lagrangian.
  1. Fertig Research Group: Multiscale Failure of Materials
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Thanks for the lecture
But, I don't quite understand, would eq.5 not be V(X, t)=V(phi^-1(xi, t), t)?
i.e., the definition of velocity at a point expressed in terms of the velocity field; which is a different definition than the eq.4
kindly illuminate

snehasish