“curl”的概念、定义、翻译、参考文献-科学参考

curl

Physics

The vector product of the gradient operator with a vector. For a vector u that has components u₁, u₂, and u₃ in the x, y, and z directions (with respective unit vectors i, j, and k), and is a function of x, y, and z, the curl is given by:

$curl u = \nabla \times u = (∂ u_{3} / ∂ y - ∂ u_{2} / ∂ z) i + (∂ u_{1} / ∂ z - ∂ u_{3} / ∂ x) j + (∂ u_{2} / ∂ x - ∂ u_{1} / ∂ y) k .$

See also divergence.

Mathematics

For a vector function of position V(r)=V_x i + V_y j + V_z k, the curl of V is the vector product of the operator del, $\nabla = i \frac{\partial}{\partial x} + j \frac{\partial}{\partial y} + k \frac{\partial}{\partial z}$ with V giving curl $V = \nabla \times V = i \times \frac{\partial V}{\partial x} + j \times \frac{\partial V}{\partial y} + k \times \frac{\partial V}{\partial z}$ which can be written in determinant form as $| \begin{matrix} i & j & k \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ V_{x} & V_{y} & V_{z} \end{matrix} | .$ If V = ∇φ‎ then curlV = 0 and if the domain of V is simply connected then curlV = 0 implies V = ∇φ‎ for a scalar field φ‎. Curl relates to the local rotation of a field; for example, if V is the velocity field of a fluid flow, a small ball of fluid will rotate in the direction of curlV, and with an angular speed half the magnitude of curlV. Compare divergence, gradient.

Electronics and Electrical Engineering

In vector calculus, a vector that characterizes the degree of rotation in the flow represented by a vector field. The vector points along the axis of rotation, with the flow in a clockwise direction when observed from a point at the end of the vector looking along it. See also div.

单词	curl
释义	curl Physics The vector product of the gradient operator with a vector. For a vector u that has components u₁, u₂, and u₃ in the x, y, and z directions (with respective unit vectors i, j, and k), and is a function of x, y, and z, the curl is given by: $curl u = \nabla \times u = (∂ u_{3} / ∂ y - ∂ u_{2} / ∂ z) i + (∂ u_{1} / ∂ z - ∂ u_{3} / ∂ x) j + (∂ u_{2} / ∂ x - ∂ u_{1} / ∂ y) k .$ See also divergence. Mathematics For a vector function of position V(r)=V_x i + V_y j + V_z k, the curl of V is the vector product of the operator del, $\nabla = i \frac{\partial}{\partial x} + j \frac{\partial}{\partial y} + k \frac{\partial}{\partial z}$ with V giving curl $V = \nabla \times V = i \times \frac{\partial V}{\partial x} + j \times \frac{\partial V}{\partial y} + k \times \frac{\partial V}{\partial z}$ which can be written in determinant form as $\| \begin{matrix} i & j & k \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ V_{x} & V_{y} & V_{z} \end{matrix} \| .$ If V = ∇φ‎ then curlV = 0 and if the domain of V is simply connected then curlV = 0 implies V = ∇φ‎ for a scalar field φ‎. Curl relates to the local rotation of a field; for example, if V is the velocity field of a fluid flow, a small ball of fluid will rotate in the direction of curlV, and with an angular speed half the magnitude of curlV. Compare divergence, gradient. Electronics and Electrical Engineering In vector calculus, a vector that characterizes the degree of rotation in the flow represented by a vector field. The vector points along the axis of rotation, with the flow in a clockwise direction when observed from a point at the end of the vector looking along it. See also div.
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