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