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moorepants committed Apr 25, 2024
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6 changes: 3 additions & 3 deletions generalized-forces.rst
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Expand Up @@ -39,7 +39,7 @@ Learning Objectives

After completing this chapter readers will be able to:

- Calculate partial velocities given generalized speeds
- Calculate partial velocities when given generalized speeds
- Calculate generalized active forces for a system of particles and rigid
bodies
- Calculate generalized inertia forces for a system of particles and rigid
Expand Down Expand Up @@ -258,7 +258,7 @@ Nonholonomic Partial Velocities
If a system is nonholonomic, it is also true that every translational and
angular velocity can be expressed uniquely in terms of the :math:`p`
independent generalized speeds (see Eq.
:math:numref:`eq-contraint-linear-form-solve`). Thus, we can also define the
:math:numref:`eq-constraint-linear-form-solve`). Thus, we can also define the
*nonholonomic partial velocities* :math:`\tilde{v}_r` and *nonholonomic partial
angular velocities* :math:`\tilde{\omega}_r` as per ([Kane1985]_, pg. 46):

Expand All @@ -269,7 +269,7 @@ angular velocities* :math:`\tilde{\omega}_r` as per ([Kane1985]_, pg. 46):
\bar{\omega} = & \sum_{r=1}^p \tilde{\omega}_r u_r + \tilde{\omega}_t
If you have found the :math:`n` holonomic partial velocities, then you can use
:math:`\mathbf{A}_n` from :math:numref:`eq-contraint-linear-form-solve` to find
:math:`\mathbf{A}_n` from :math:numref:`eq-constraint-linear-form-solve` to find
the nonholonomic partial velocities with:

.. math::
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4 changes: 2 additions & 2 deletions motion.rst
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Expand Up @@ -779,7 +779,7 @@ independent generalized speeds and :math:`\bar{u}_r` as a vector of dependent
generalized speeds, the nonholonomic constraints can be written as:

.. math::
:label: eq-contraint-linear-form
:label: eq-constraint-linear-form
\bar{f}_n(\bar{u}_s, \bar{u}_r, \bar{q}, t) =
\mathbf{A}_r(\bar{q}, t) \bar{u}_r +
Expand All @@ -789,7 +789,7 @@ generalized speeds, the nonholonomic constraints can be written as:
or

.. math::
:label: eq-contraint-linear-form-solve
:label: eq-constraint-linear-form-solve
\bar{u}_r = \mathbf{A}_r^{-1}\left(-\mathbf{A}_s \bar{u}_s - \bar{b}_{rs}\right) \\
\bar{u}_r = \mathbf{A}_n \bar{u}_s + \bar{b}_n
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2 changes: 1 addition & 1 deletion nonholonomic-eom.rst
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Expand Up @@ -82,7 +82,7 @@ and :math:`u_r` can be solved for as so:
\bar{u}_r = -\mathbf{M}_n(\bar{q}, t)^{-1}\bar{g}_n(\bar{u}_s, \bar{q}, t)
which is the same as Eq. :math:numref:`eq-contraint-linear-form-solve` we
which is the same as Eq. :math:numref:`eq-constraint-linear-form-solve` we
originally developed:

.. math::
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