Consider the motion of a body given by

,

for times and where and are constants with dimension of length and is a constant with a dimension of time.

a) What constraints does the requirement of local invertibility place on constants and ?

b) Are the constraints you obtained above sufficient to ensure that the motion s a 1-1 mapping? Explain.

For the remainder of the problem assume that the reference domain is limited to , where .

c) Let us visualize the deformation for the special case . Consider a regular grid with spacing in the reference domain. Draw the shape of the deformed grid in the deformed configuration in the plane at times .

21 X+X3 , 12 = (/ 2B(1 + t/to) Carctan(X2/X1), 13 = B(1 + t/to) X t 0 21 X+X3 , 12 = (/ 2B(1 + t/to) Carctan(X2/X1), 13 = B(1 + t/to) X t 0