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Problem 3. Let F F* be a change of frame characterized by a frame-rotation Q = Q(t) and the frame-translation c(ta) for some a
Problem 3. Let F F* be a change of frame characterized by a frame-rotation Q = Q(t) and the frame-translation c(ta) for some a R. Let T* = T(x*, t) and T = T(x, t) be the (Eulerian) Cauchy stress tensor at time t, for a continuum body B, with respect to the frames F* and F, respectively. In addition, assume that both frames are respectively endowed with Cartesian coordinate systems (x1, x2, x313) and (x1, x2, x3) with the origin coinciding with the origin of the coordinate system for the reference configuration (and corresponding unit orthonormal basis {et, ez, e} and {, 2, 3}). In this setting, we have Tmn (x1, x2, xz, t) = e (T* (x*, t) en), * * Tmn (x1, x2, x3,t) = em (T(x, t) en). Prove that T (x, xz, xz, t) = Tij(x1, x2, x3, t) for all i, j = 1, 2, 3.
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