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examples/example_11/example_11.md

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@@ -4,8 +4,7 @@ The <a href="https://github.com/projectchrono/chrono">Chrono</a> library is the
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to simulate robots and create environments for reinforcement learning agents. As such, knowing your way around
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Chrono is essential. However, Chrono is a relatively large library with many components and therefore not necessarily easy
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to grasp. In a series of examples, we will see main components of the library that _bitrl_ utilizes.
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You should have compiled Chrono with <a href="https://irrlicht.sourceforge.io/">Irrlicht</a> support.
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Note that you should have compiled Chrono with <a href="https://irrlicht.sourceforge.io/">Irrlicht</a> support in order to be able to run this example.
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The main interface for creating rigid bodies in Chrono is the <a href="https://api.projectchrono.org/9.0.0/classchrono_1_1_ch_body.html">ChBody</a>
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class. You can also find this <a href="https://api.projectchrono.org/9.0.0/rigid_bodies.html"> Rigid Bodies</a> helpful.
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T = (R, p)
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$$
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where $R$ is a rotation matrix and $p$ is a translation vector. Chrono uses quaternions to express rotations but
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where \f$R\f$ is a rotation matrix and \f$p\f$ is a translation vector. Chrono uses quaternions to express rotations but
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let's keep the discussion simple. Then
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@code
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ref_frame = ( R_wr , p_wr )
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child_frame_in_ref = ( R_rc , p_rc )
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@endcode
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where $p_{wr} = (0,0,0)$, $p_{rc}=(0, 0, 0.22)$. When we multiply the two frames we do something equivalent to
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where \f$p_{wr} = (0,0,0)\f$, \f$p_{rc}=(0, 0, 0.22)\f$. When we multiply the two frames we do something equivalent to
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@code
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(R_wr, p_wr) * (R_rc, p_rc) = ( R_wr * R_rc , p_wr + R_wr p_rc )
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@endcode
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However, the two frames are not rotated so both $R_{wr}$ and $R_{rc}$ are actually the identity matrix. Thus, we end up with
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However, the two frames are not rotated so both \f$R_{wr}\f$ and \f$R_{rc}\f$ are actually the identity matrix. Thus, we end up with
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$$
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p_{wr} + R_{wr} p_{rc} = (0, 0, 0.22)

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