Add cards.xml model.

PiperOrigin-RevId: 571341445
Change-Id: I3a02bb01099cacb62e0c599e6198ed90b48baad0
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Yuval Tassa
2023-10-06 08:12:51 -07:00
committed by Copybara-Service
parent a9b761ee1b
commit 7b7cf5e86c
57 changed files with 756 additions and 1 deletions
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@@ -265,12 +265,17 @@ viscosity and scales with the second power of the velocity. It can be written as
Where :math:`C_D` is a drag coefficient, and :math:`A_D` is a reference surface area (e.g. a measure of the projected
area on the plane normal to the flow), and :math:`I_D` a reference moment of inertia.
.. youtube:: nljr0X79vI0
:align: right
:width: 50%
Even for simple shapes, the terms :math:`C_D`, :math:`A_D` and :math:`I_D` need to be tuned to the problem-specific
physics and dynamical scales :cite:p:`duan2015`. For example, the drag coefficient :math:`C_D` generally decreases with
increasing Reynolds numbers, and a single reference area :math:`A_D` may not be sufficient to account for the skin
drag for highly irregular or slender bodies. For example, experimental fits are derived from problems ranging from
falling playing cards :cite:p:`wang2004,andersen2005a,andersen2005b` to particle transport :cite:p:`loth2008,
bagheri2016`.
bagheri2016`. See screen capture of the
`cards.xml <https://github.com/deepmind/mujoco/blob/main/model/card/cards.xml>`__ model on the right.
We derive a formula for :math:`\mathbf{f}_\text{D}` based on two surfaces :math:`A^\text{proj}_\mathbf{v}` and
:math:`A_\text{max}`. The first, :math:`A^\text{proj}_\mathbf{v}`, is the cylindrical projection of the body onto a