imaginary axis การใช้

• At gain 3, the poles cross the imaginary axis.
• For a flow, it will occur when there are eigenvalues on the imaginary axis.
• Sometimes the presence of poles on the imaginary axis creates a situation of marginal stability.
• Are equivalent if one permits the coordinate to take on imaginary axis, and vice versa.
• The origin of the complex plane can be referred as the point where real axis and imaginary axis intersect each other.
• This vertical axis is often called the " imaginary axis " and is denoted, \ scriptstyle \ mathbb { I }, or.
• A " Hopf bifurcation " arises when these two eigenvalues cross the imaginary axis because of a variation of the system parameters.
• Because of the minus sign in some of the formulas below, it is also called the " imaginary axis " of the hyperbola.
• Reactive power does not do any work, so it is represented as the "'imaginary axis "'of the vector diagram.
• It is particularly hard to design robust controllers realizing the desired performance properties for unstable, integrating and oscillatory processes having poles near the imaginary axis.
• However, if and are kept on the real and imaginary axis, respectively, then the Jacobi elliptic functions will be real functions when is real.
• So the anti-Stokes line can be taken to be the imaginary axis, and the Stokes line can be taken to be the real axis.
• The argument of the square root is a non-positive real number if and only if belongs to one of the intervals and of the imaginary axis.
• And since sin y / y is the zeroth spherical Bessel function, the above would involve the sph bess function along the imaginary axis, K _ 0.
• The " n " poles of this expression occur on a circle of radius ? c at equally-spaced points, and symmetric around the imaginary axis.
• To be able to analyze systems with poles on the imaginary axis, the Nyquist Contour can be modified to avoid passing through the point 0 + j \ omega.
• It vanishes on the integers; however, it grows exponentially on the imaginary axis with a growth rate of } }, and indeed it is not identically zero.
• So is it possible to project an imaginary axis on a 3D, maybe as ( x, y, z, i ), n-dimensional Euclidean space?
• Consider what happens, for example when " z " takes values on a circle of diameter 1 / " R " tangent to the imaginary axis.
• If x > r, the function turns into an imaginary number, so you can imagine a third imaginary axis perpendicular to the x and y on the cartesian plane.