= Rivlin-Ericksen tensor
{c}
{title2=$A_1=K+K^T,\quad A_{j+1}=D_tA_j+A_jK+K^TA_j$}
Using the component-first <velocity gradient> $K_{ij}=\partial v_i/\partial x_j$, the Rivlin-Ericksen tensors are defined by the displayed recurrence. In particular $A_1$ is twice the <rate-of-strain tensor>. These tensors transform objectively under time-dependent rigid observer changes. With this convention the <upper-convected derivative> of $A_1$ is $A_2-2A_1^2$, an identity useful in the slow-flow expansion of a <second-order fluid>.
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