Definition:Rotational Vector Field

Definition

Let $R$ be a region of space.

Let $\mathbf V$ be a vector field acting over $R$.

Then $\mathbf V$ is a rotational vector field if and only if the curl of $\mathbf V$ is not everywhere zero:

$\curl \mathbf V \not \equiv \bszero$

That is, if and only if $\mathbf V$ is not conservative.

Also see

• Definition:Rotational Motion

Sources

• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {V}$: Further Applications of the Operator $\nabla$: $7$. The Classification of Vector Fields: $\text {(iii)}$