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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -246,18 +246,6 @@ where:
246246 \bar {g} = \frac {d\mathbf {M}\bar {v}}{dt}\bigg\rvert _{\dot {\bar {u}}=\bar {0 }} =
247247 \left (\dot {\mathbf {M}} \mathbf {T} + \mathbf {M} \dot {\mathbf {T}}\right ) \bar {u}
248248
249- The equations of motion then take this form:
250-
251- .. math ::
252-
253- \mathbf {M}_d\dot {\bar {u}} + \bar {g}_d =
254- -\mathbf {T}^T \mathbf {M} \mathbf {T} \dot {\bar {u}} +
255- \mathbf {T}^T\left (\bar {F} - \bar {g}\right )
256- = \bar {0 }
257-
258- These equations are equivalent to Kane's and Lagrange's dynamical differential
259- equations.
260-
261249 .. note ::
262250
263251 It is worth noting that with the chain rule you can compute
@@ -275,6 +263,21 @@ equations.
275263 \mathbf {M} = \left [\begin {array}{c|c|c}\bar {M}_i & \ldots & \bar {M}_{6 \nu } \end {array}\right ], \quad
276264 \mathbf {T} = \left [\begin {array}{c|c|c}\bar {T}_j & \ldots & \bar {T}_n \end {array}\right ]
277265
266+ It is then clear that :math: `\bar {g}(\bar {u}, \bar {q})` are inertial forces
267+ that are stricly a function of configuration and velocity.
268+
269+ The equations of motion then take this form:
270+
271+ .. math ::
272+
273+ \mathbf {M}_d\dot {\bar {u}} + \bar {g}_d =
274+ -\mathbf {T}^T \mathbf {M} \mathbf {T} \dot {\bar {u}} +
275+ \mathbf {T}^T\left (\bar {F} - \bar {g}\right )
276+ = \bar {0 }
277+
278+ These equations are equivalent to Kane's and Lagrange's dynamical differential
279+ equations.
280+
278281Example Formulation
279282===================
280283
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