Cauchy's equation in terms of material acceleration

[Adam Venter]

Does anyone know which formula is used or how to arrive at the righthand side of the equation below, which is the dot product of del and rho*a 2nd order tensor(V V).
. represents dot product
and X a vector quantity
This problem is in connection with transforming cauchy's equation in terms of the material acceleration

del . (rho*V V) = {V*del . (rho*V) } + {rho*(V . del)*V}

Thanks

 

[Chestermiller]

Does anyone know which formula is used or how to arrive at the righthand side of the equation below, which is the dot product of del and rho*a 2nd order tensor(V V).
. represents dot product
and X a vector quantity
This problem is in connection with transforming cauchy's equation in terms of the material acceleration

del . (rho*V V) = {V*del . (rho*V) } + {rho*(V . del)*V}

Thanks

It's basically application of the derivative of a product rule in a situation in which you are dealing with vectors. The easiest way to prove to yourself that the identity is correct is to write it out in cartesian component form.

Chet

 

[Adam Venter]

It's basically application of the derivative of a product rule in a situation in which you are dealing with vectors. The easiest way to prove to yourself that the identity is correct is to write it out in cartesian component form.

Chet

Thanks will give that a go