move notes out of year subfolders

uni/mmme/2046_dynamics_and_control/.n2w.yml

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+itags: [ mmme2046 ]

uni/mmme/2046_dynamics_and_control/control.md

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+---
+author: Akbar Rahman
+date: \today
+title: MMME2046 // Control
+tags: [ mmme2046, uon, uni, control ]
+uuid: 
+---
+
+# System and Block Diagrams
+
+# Laplace Transform
+
+$$F(s) = \mathscr L {F(t)} = \int^\infty_0 f(t)e^{-st} \mathrm{d}t$$
+
+where $s = \alpha + j\omega$
+
+The function $F(s)$ is often much easier to manipulate than periodic function $f(t)$.
+
+## Final Value Theorem
+
+As $f(t)$ tends to infinity, $sF(s)$ tends to 0.
+
+## Example
+
+$$\dot x_o = ax_o = ax_i$$
+
+where $x_o$ is the output and $x_i$ is the input
+
+Take the Laplace transform:
+
+$$sX_o(s) + aX_o(s) = aX_i(s)$$
+
+Rearrange to get equation for the transfer function:
+
+$$G(s) = \frac{X_o}{X_i} = \frac{a}{s+a}$$
+
+$$ X_o = GX_i $$
+
+If $X_i$ is a unit step, then:
+
+$$X_i = \frac1s$$
+
+and
+
+$$X_o = \frac{a}{s(s+a)}$$
+
+Taking the inverse gives:
+
+$$X_0 = 1 - e^{-at}$$
+

uni/mmme/2046_dynamics_and_control/dynamics.md

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+---
+author: Akbar Rahman
+date: \today
+title: MMME2046 // Dynamics
+tags: [ mmme2046, uon, uni, dynamics ]
+uuid: 98a5449a-02d3-492c-9d0e-3d3eb74baab5
+---
+
+# Machine Dynamics
+
+- 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)