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ii_pof

Purpose

Transformations between the three accepted pole formats.

Syntax

```[pob] = ii_pof(poa,DesiredFormatNumber)
[pob] = ii_pof(poa,DesiredFormatNumber,SortFlag)
```

Description

The Structural Dynamics Toolbox deals with real models so that poles are either real or come in conjugate pairs

{ λ,λ }= { a ± i b} = {−ζω±ω
 1−ζ2
}

Poles can be stored in three accepted formats which are automatically recognized by ii_pof(see warnings below for exceptions).

Because non-real poles come in conjugate pairs with conjugate eigenvectors, it is generally easier to only view the positive-imaginary and real poles, as done in the two other formats.

Format 2: real and imaginary part

po = [
 a b ⋮ ⋮
]   for example
 po=[-0.0200 1.9999 -1.0000 0.0000]

Format 3: frequency ω and damping ratio ζ

po = [
 ω1 ζ1 ⋮ ⋮
]   for example
 po=[ 2.0000 0.0100 −1.0000 1.0000]

To sort the poles while changing format use an arbitrary third argument SortFlag.

Warnings

The input format is recognized automatically. An error is however found for poles in input format 2 (real and imaginary) with all imaginary below 1 and all real parts positive (unstable poles). In this rare case you should change your frequency unit so that some of the imaginary parts are above 1.

Real poles are always put at the end. If you create your own residue matrices, make sure that there is no mismatch between the pole and residue order (the format for storing residues is described in section 5.6).