Update content - 2026-10-14

content/article/oomen18_advan_motion_contr_precis_mechat.md

@@ -39,14 +39,14 @@ In the frequency range that is relevant for control, the dynamical behavior is m
 In particular, the mechanics can typically be described as:
 
 \begin{equation}
-G\_m = \sum\_{i=1}^{n\_{RB}} \frac{c\_i b\_i^T}{s^2} + \sum\_{n\_{RB} + 1}^{n\_s} \frac{c\_i b\_i^T}{s^2 + 2\xi \omega\_i s + \omega\_i^2}
+G\_m = \sum\_{i=1}^{n\_{RB}} \frac{c\_i b\_i^T}{s^2} + \sum\_{n\_{RB} + 1}^{n\_s} \frac{c\_i b\_i^T}{s^2 + 2\zeta \omega\_i s + \omega\_i^2}
 \end{equation}
 
 where the first term refers to rigid body modes and the second term to flexible modes.
 
 -   \\(n\_{RB}\\) is the number of rigid body modes
 -   \\(c\_i \in \mathbb{R}^{n\_y}\\) and \\(b\_i \in \mathbb{R}^{n\_u}\\) are associated with the mode shapes
--   \\(\xi\_i, \omega\_i \in \mathbb{R}\_+\\)
+-   \\(\zeta\_i, \omega\_i \in \mathbb{R}\_+\\)
 
 In traditional positioning systems, the number of actuators \\(n\_u\\) and sensors \\(n\_y\\) equals the number of rigid body modes \\(n\_{RB}\\) and are positioned such that the matrix \\(\sum\_{i=1}^{n\_{RB}} c\_i b\_i^T\\) is invertible.
 In this case, matrices \\(T\_u\\) and \\(T\_y\\) can be selected such that: