From 7e6a9e03fa8f66dcba3fe6d2f6986ca5045fbe82 Mon Sep 17 00:00:00 2001 From: Alexander Fabisch Date: Sun, 29 Sep 2024 14:01:23 +0200 Subject: [PATCH] Link references --- doc/source/user_guide/transformations.rst | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/doc/source/user_guide/transformations.rst b/doc/source/user_guide/transformations.rst index d695605a..d3ab7164 100644 --- a/doc/source/user_guide/transformations.rst +++ b/doc/source/user_guide/transformations.rst @@ -196,13 +196,13 @@ coordinates of transformation and typically we use the variable name Stheta. .. warning:: Note that we use the screw theory definition of exponential coordinates - and :math:`se(3)` (see next section) used by Paden (1985), Lynch and Park - (2017), and Corke (2017). They separate the parameter :math:`\theta` from + and :math:`se(3)` (see next section) used by Lynch and Park (2017) [1]_, + and Corke (2017) [2]_. They separate the parameter :math:`\theta` from the screw axis. Additionally, they use the first three components to encode rotation and the last three components to encode translation. There is an - alternative definition used by Eade (2017) and Sola et al. (2018). They use - a different order of the 3D vector components and they do not separate - :math:`\theta` from the screw axis in their notation. + alternative definition used by Eade (2017) [3]_ and Sola et al. (2018) + [4]_. They use a different order of the 3D vector components and they do + not separate :math:`\theta` from the screw axis in their notation. --------------------------- Logarithm of Transformation @@ -251,8 +251,9 @@ Twist We call spatial velocity (translation and rotation) **twist**. Similarly to the matrix logarithm, a twist :math:`\mathcal{V} = \mathcal{S} \dot{\theta}` -is described by a screw axis :math:`S` and a scalar :math:`\dot{\theta}` -and :math:`\left[\mathcal{V}\right] = \left[\mathcal{S}\right] \dot{\theta} \in se(3)` +is described by a screw axis :math:`\mathcal S` and a scalar +:math:`\dot{\theta}` and +:math:`\left[\mathcal{V}\right] = \left[\mathcal{S}\right] \dot{\theta} \in se(3)` is the matrix representation of a twist. ----------------