Typo and minor changes.

PiperOrigin-RevId: 574403633
Change-Id: I1798f91e27911e351ee99c749c6dd62d851b61cf
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Google DeepMind
2023-10-18 01:52:45 -07:00
committed by Copybara-Service
parent 8f9c690c85
commit 98cc3a6fb2
+5 -5
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@@ -26,7 +26,7 @@ to positive values. These parameters correspond to the density :math:`\rho` and
Inertia model
-------------
In this model, the shape of each body, for fluid dynamics purposes, is assumed to be the *equivalent inertia box*,
In this model the shape of each body, for fluid dynamics purposes, is assumed to be the *equivalent inertia box*,
which can also be visualized. For a body with mass :math:`\mathcal{M}` and inertia matrix :math:`\mathcal{I}`, the
half-dimensions (i.e. half-width, half-depth and half-height) of the equivalent inertia box are
@@ -34,17 +34,17 @@ half-dimensions (i.e. half-width, half-depth and half-height) of the equivalent
\begin{align*}
r_x = \sqrt{\frac{3}{2 \mathcal{M}} \left(\mathcal{I}_{yy} + \mathcal{I}_{zz} - \mathcal{I}_{xx} \right)} \\
r_y = \sqrt{\frac{3}{2 \mathcal{M}} \left(\mathcal{I}_{zz} + \mathcal{I}_{xx} - \mathcal{I}_{yy} \right)} \\
r_z = \sqrt{\frac{3}{2 \mathcal{M}} \left(\mathcal{I}_{xx} + \mathcal{I}_{yy} - \mathcal{I}_{zz} \right)}.
r_z = \sqrt{\frac{3}{2 \mathcal{M}} \left(\mathcal{I}_{xx} + \mathcal{I}_{yy} - \mathcal{I}_{zz} \right)}
\end{align*}
Let :math:`\mathbf{v}` and :math:`\boldsymbol{\omega}` denote the linear and angular body velocity of the body in
the body-local frame (aligned with the equivalent inertia box). The force :math:`\mathbf{f}_{\text{inertia}}` and
torque :math:`\mathbf{g}_{\text{inertia}}` exerted by the fluid onto the solid are the sum of of the terms
torque :math:`\mathbf{g}_{\text{inertia}}` exerted by the fluid onto the solid are the sum of the terms
.. math::
\begin{align*}
\mathbf{f}_{\text{inertia}} &= \mathbf{f}_D + \mathbf{f}_V \\
\mathbf{g}_{\text{inertia}} &= \mathbf{g}_D + \mathbf{g}_V.
\mathbf{g}_{\text{inertia}} &= \mathbf{g}_D + \mathbf{g}_V
\end{align*}
Here subscripts :math:`D` and :math:`V` denote quadratic Drag and Viscous resistance.
@@ -455,7 +455,7 @@ Given this reference moment of inertia, the angular drag torque is computed as:
Here :math:`\mathbf{I}_\text{max}` is a vector with each entry equal to the maximal component of :math:`\mathbf{I}_D`.
Finally, the viscous resistance terms, also known as linear drag, well approvimate the fluid forces for Reynolds
Finally the viscous resistance terms, also known as linear drag, well approvimate the fluid forces for Reynolds
numbers around or below :math:`O(10)`. These are computed for the equivalent sphere with Stokes' law
:cite:p:`stokes1850,lamb1932`: