mmme2046 l3 w05/42

uni/mmme/2xxx/2046_dynamics_and_control/dynamics.md

@@ -11,5 +11,46 @@ uuid: 98a5449a-02d3-492c-9d0e-3d3eb74baab5
 - Rigid Body - Distances between any two particles on a body remain constant---in real life we are
                looking for negligible deformation
 
+# Lecture 2 (W04/41)
+
+## Relative Motion
+
+![](./images/vimscrot-2022-10-17T09:09:23,080550083+01:00.png)
+
+where $_{BA}$ is read as "$B$ as seen by $A$".
+
+These equations must be treated as vectors.
+
+# Lecture 3 (W05/42)
+
+## Instantaneous Centre of Rotation
+
+This is a point with zero velocity at any particular moment.
+
+![](./images/vimscrot-2022-10-17T09:13:09,972195575+01:00.png)
+
+$$v_A = 0$$
+
+$$v_B = v_{BA}$$
+
+To find the centre of rotation you can draw to perpendicular lines to velocities from two non
+stationary points.
+The centre of rotation will be where the lines intersect.
+
+![](./images/vimscrot-2022-10-17T09:14:37,194818034+01:00.png)
+
+## Point Velocity Projections on Joining Axis
+
+Take two points $A$ and $B$ and their velocities at one instant
+
+\begin{align}
+v_B &= v_A = v_{BA} \\
+\text{then } \pmb{v_B} || AB &= \pmb{v_A} || AB + \pmb{v_{BA} || AB \\
+\text{but } \pmb{v_BA} || AB &\equiv 0 \text{(since $\pmb{v_BA} \perp AB$)} \\
+\text{or } \pmb{v_B| || AB &= \pmb{v_A} || AB \\
+v_B\cos\beta = v_A\cos\alpha \\
+\end{align}
+
+# zack.jpg
 
 ![zack.jpg](./images/zack.jpg)