diff --git a/motion.rst b/motion.rst index 718219c3..a9be85e2 100644 --- a/motion.rst +++ b/motion.rst @@ -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