1. The problem statement, all variables and given/known data 2. Relevant equations x = (x1,x2,x3) are the coordinates of the current configuration and X = (X1,X2,X3) are the coordinates of the reference configuration where x = y(X,t) where y is a deformation of X. 3. The attempt at a solution (a) taking the partial derivatives of xi with respect to t: ∂(x1)/∂t = αX2 + 2(α^2)X3*t ∂(x2)/∂t = 2(α^2)*X1*t + αX3 ∂(x3)/∂t = αX1 +2(α^2)X2t so v(X,t) = (αX2 + 2(α^2)X3*t , 2(α^2)*X1*t + αX3 , αX1 +2(α^2)X2t ) (1) v((d,d,d),0) = ( αd , αd , αd ) a(X,t) = ∂v/∂t = ( 2(α^2)X3, 2(α^2)*X1 , 2(α^2)X2 ) (2) a((d,d,d),0) = ( 2(α^2)d , 2(α^2)*d, 2(α^2)d ) (b) for this part we know that x = (d,d,d) , so we wan't to find the X that corresponds to this point so we can plug it into the functions v(X,t) and a(X,t). rearranging the three equations of motion: X1 = x1 - αX2t - (α^2)X3t^2 (a) X2 = x1 - αX3t - (α^2)X1t^2 (b) X3 = x1 - αX1t - (α^2)X2t^2 (c) now, subbing (b) and (c) into (a) we have: X1 = x1 - α( x1 - αX3t - (α^2)X1t^2 )t - (α^2)( x1 - αX1t - (α^2)X2t^2 )t^2 from the above it seems like like I won't be able to express X1 solely in terms of spatial coordinates because if I expand the second and third term I won't be able to get rid of X3 and X2. Any help would be appreciated.