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Correct sign error in rolling without slip explanation.
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moorepants committed Mar 14, 2024
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8 changes: 4 additions & 4 deletions motion.rst
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Expand Up @@ -344,19 +344,19 @@ and the angular velocity to give the velocity of :math:`C`:

.. math::
{}^N\bar{v}^{C} = & \dot{q}_1\hat{n}_x - \dot{q}_2 \hat{n}_z \times -r\hat{n}_y \\
{}^N\bar{v}^{C} = & \dot{q}_1\hat{n}_x - \dot{q}_2 r \hat{n}_x
{}^N\bar{v}^{C} = & \dot{q}_1\hat{n}_x + \dot{q}_2 \hat{n}_z \times -r\hat{n}_y \\
{}^N\bar{v}^{C} = & \dot{q}_1\hat{n}_x + \dot{q}_2 r \hat{n}_x
Applying the motion constraint and knowing that :math:`{}^N\bar{v}^{G} = 0`
gives us this scalar constraint equation:

.. math::
\dot{q}_1 - \dot{q}_2 r = 0
\dot{q}_1 + \dot{q}_2 r = 0
This is a scalar constraint equation that ensures rolling without slip and
involves the time derivatives of the coordinates. It is integrable and thus
actually a holonomic constraint, i.e. :math:`q_1 - q_2 r = 0`. General rolling
actually a holonomic constraint, i.e. :math:`q_1 + q_2 r = 0`. General rolling
without slip in three dimensions will be nonholonomic. Take care to calculate
the relative velocities of the two points fixed in each of the bodies in
rolling contact that are located at the contact point at that *instance of
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