From 24634aae5105fdf843df24abd02838adc99e88a1 Mon Sep 17 00:00:00 2001 From: Alvie Rahman Date: Mon, 17 Oct 2022 10:49:09 +0100 Subject: [PATCH] mmme2046 l3 w05/42 --- .../2046_dynamics_and_control/dynamics.md | 41 ++++++++++++++++++ ...ot-2022-10-17T09:09:23,080550083+01:00.png | Bin 0 -> 63067 bytes ...ot-2022-10-17T09:13:09,972195575+01:00.png | Bin 0 -> 17680 bytes ...ot-2022-10-17T09:14:37,194818034+01:00.png | Bin 0 -> 20069 bytes .../lecture_slides/MD Lecture 2 delivered.pdf | Bin 0 -> 1773644 bytes .../lecture_slides/MD Lecture 3.pdf | Bin 0 -> 942644 bytes 6 files changed, 41 insertions(+) create mode 100644 uni/mmme/2xxx/2046_dynamics_and_control/images/vimscrot-2022-10-17T09:09:23,080550083+01:00.png create mode 100644 uni/mmme/2xxx/2046_dynamics_and_control/images/vimscrot-2022-10-17T09:13:09,972195575+01:00.png create mode 100644 uni/mmme/2xxx/2046_dynamics_and_control/images/vimscrot-2022-10-17T09:14:37,194818034+01:00.png create mode 100644 uni/mmme/2xxx/2046_dynamics_and_control/lecture_slides/MD Lecture 2 delivered.pdf create mode 100644 uni/mmme/2xxx/2046_dynamics_and_control/lecture_slides/MD Lecture 3.pdf diff --git a/uni/mmme/2xxx/2046_dynamics_and_control/dynamics.md b/uni/mmme/2xxx/2046_dynamics_and_control/dynamics.md index 437b9f6..5fb682e 100755 --- a/uni/mmme/2xxx/2046_dynamics_and_control/dynamics.md +++ b/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) diff --git a/uni/mmme/2xxx/2046_dynamics_and_control/images/vimscrot-2022-10-17T09:09:23,080550083+01:00.png b/uni/mmme/2xxx/2046_dynamics_and_control/images/vimscrot-2022-10-17T09:09:23,080550083+01:00.png 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