Erratum to: A note on the motion representation and configuration update in time stepping schemes for the constrained rigid body

1 Erratum to: BIT Numer Math DOI 10.1007/s10543-015-0580-y

Due to typesetting errors, some corrections marked in the proof were not carried out.

• 1. The line after Eq. (6): The argument in $\exp \widehat{\varvec{\xi }}$ should be in boldface.

• 2. The second line after Eq. (8): Superscripts in the equation should not be in boldface: $\mathbf {V}^{\text {m}}=(\varvec{\omega }^{\text {b}},\dot{\mathbf {r}})$.

• 3. The third line after (8): The vector should be in boldface: $\varvec{\omega }^{\text {b}}$.

• 4. The fourth line after Eq. (11): The superscripts should not be in boldface: $( \varvec{\Theta }_{0}\varvec{\omega }^{\text {b}},m\dot{ \mathbf {r}}) \in so^{*}\left( 3\right) \times {\mathbb {R}}^{3}$.

• 5. The Eq. (12) should be

  $$\begin{aligned} \varvec{\Theta }_{0}\dot{\varvec{\omega }}^{\text {b}}+\varvec{\omega }^{ \text {b}}\times \varvec{\Theta }_{0}\varvec{\omega }^{\text {b}}= & {} \mathbf {0}\\ m\ddot{\mathbf {r}}= & {} \mathbf {0}. \nonumber \end{aligned}$$

  (12)

• 6. The Eq. (17) should be

  $$\begin{aligned} \varvec{\Theta }_{0}\dot{\varvec{\omega }}^{\text {b}}+\varvec{\omega }^{\text {b}}\times \varvec{\Theta }_{0}\varvec{\omega }^{\text {b}}= & {} \mathbf {0}\\ m\dot{\mathbf {v}}^{\text {b}}+m\varvec{\omega }^{\text {b}}\times \mathbf {v}^{ \text {b}}= & {} \mathbf {0}. \nonumber \end{aligned}$$

  (17)

• 7. The first line after Eq. (18): The equation should be $\mathbf {J} \left( C\right) \dot{\mathbf {V}}=\varvec{\eta }\left( C,\mathbf {V}\right)$.

• 8. The Eq. (23) should read

  $$\begin{aligned} \mathbf {J}\dot{\mathbf {V}}^{\text {b}}=\mathbf {R(}\widehat{\varvec{\omega }} \widehat{\varvec{\omega }}\mathbf {p}+\widehat{\varvec{\omega }}\mathbf {v}),\,\,\, \text { with }\,\,{\mathbf {J}}= ( {\mathbf {R}}{\widehat{\mathbf {p}}} -{\mathbf {R}} ). \end{aligned}$$

  (23)

• 9. The second line of the second paragraph in Sect. 5.3: It should be $\mathbf {p}\times \varvec{\omega }_{0}^{\text {b}}+(0,1,0)$ m/s.