Add cards.xml model.
PiperOrigin-RevId: 571341445 Change-Id: I3a02bb01099cacb62e0c599e6198ed90b48baad0
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@@ -265,12 +265,17 @@ viscosity and scales with the second power of the velocity. It can be written as
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Where :math:`C_D` is a drag coefficient, and :math:`A_D` is a reference surface area (e.g. a measure of the projected
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area on the plane normal to the flow), and :math:`I_D` a reference moment of inertia.
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.. youtube:: nljr0X79vI0
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:align: right
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:width: 50%
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Even for simple shapes, the terms :math:`C_D`, :math:`A_D` and :math:`I_D` need to be tuned to the problem-specific
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physics and dynamical scales :cite:p:`duan2015`. For example, the drag coefficient :math:`C_D` generally decreases with
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increasing Reynolds numbers, and a single reference area :math:`A_D` may not be sufficient to account for the skin
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drag for highly irregular or slender bodies. For example, experimental fits are derived from problems ranging from
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falling playing cards :cite:p:`wang2004,andersen2005a,andersen2005b` to particle transport :cite:p:`loth2008,
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bagheri2016`.
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bagheri2016`. See screen capture of the
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`cards.xml <https://github.com/deepmind/mujoco/blob/main/model/card/cards.xml>`__ model on the right.
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We derive a formula for :math:`\mathbf{f}_\text{D}` based on two surfaces :math:`A^\text{proj}_\mathbf{v}` and
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:math:`A_\text{max}`. The first, :math:`A^\text{proj}_\mathbf{v}`, is the cylindrical projection of the body onto a
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