BE 110 An Introduction to Biomechanics Fall 2005 Homework Assignment #8 Due THURSDAY 12/01/05, 8AM before class 1. Practice Problems- Show that the material derivative of a volume integral DDtA(x,y,z,t) dVV(t)∫=dAdt+A∂vi∂xi⎛ ⎝ ⎜ ⎞ ⎠ ⎟ dVV(t)∫where A(x,y,z,t) is a continuously differentiable function. Note that this relationship can be applied to different physical principles, such as conservation of mass (in which case A = ρthe mass density), or conservation of momentum (in which case A needs to be replaced by the vector component Ai= ρvi). See section 10.4. on page 215-217. - The material derivative can be used to find the boundary condition for an object suspended in a fluid. This is a useful theorem for analysis of particle motions. See problem 10.7. and 10.8. - Show that the permutation symbol is an isotropic tensor, i.e. the tensor components remain the same under a permissible orthogonal transformation. A permissible transformation refers to the fact that the orientation of the axis system does not change during the transformation, i.e. a right-
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