Correction to: Multibody System Dynamics (2023) https://doi.org/10.1007/s11044-023-09898-5

Equations 62–64 were correct as the formula was deemed wrong. The updated equations are as follows:

$$ \delta W_{i}=M_{i} \delta \theta =M_{i} \frac{\partial \theta}{\partial \mathbf{q}} \delta \mathbf{q}=\mathbf{Q}_{i}^{\top} \delta \mathbf{q}, $$
(62)
$$ \mathbf{Q}_{u}=u\left (\frac{\partial \theta}{\partial \mathbf{q}}\right )^{\top}, $$
(63)
$$ \mathbf{Q}_{d}=f_{d}\left (\frac{\partial \theta}{\partial \mathbf{q}}\right )^{\top}. $$
(64)

The symbol \(\omega\) in the sentence just before Eq. (66) and in Eq. (66) is changed to \(\mathbf{v}\) to avoid misunderstanding. The following paragraph contains that symbol change.

Introducing the generalized velocities \(\mathbf{v} = \dot{\mathbf{q}}\) as additional variables transforms the second-order differential equation for \(\mathbf{q}\) into a first-order system

$$\begin{pmatrix} \mathbf{I} & \mathbf{0} \\ \mathbf{0} & \mathbf{M} \\\end{pmatrix} \begin{pmatrix} \dot{\mathbf{q}} \\ \dot{\mathbf{v}} \\\end{pmatrix}=\begin{pmatrix} \mathbf{v} \\ \mathbf{Q}_{u} + \mathbf{Q}_{d} - \mathbf{Q}_{k} \\\end{pmatrix}. $$
(66)