Definition of lead and lag and direction of rotation

Lead and Lag

Take the following figure as an example

Can be so understood, the curve of $t> 0$ is the waveform of the past time.

It follows from this, the curve of $t <0$ is the future waveform.

From the perspective of time, looking at the future from the past, when a value is satisfied, $u$ reaches before $i$. So $u$ leads $i$.

Direction

In theory, it can be chosen arbitrarily.

In engineering, take the counterclockwise direction.

Mathematically, taking the counterclockwise direction is easy to unify with the complex plane.

Take the following figure as an example

From the figure, $c$ lags $b$ lags $a$.

After Clark transformation, the $\alpha$ axis is the real axis, and the $\beta$ axis is the imaginary axis.

Mathematically from the real axis to the imaginary axis is generally counterclockwise, so from the $\alpha$ axis to the $\beta$ axis is also counterclockwise.

End.🍜