ME3120 · Dynamic Modelling
Theme 1 · Foundations
What a dynamic model is
Where the whole course begins: what it means to turn a moving machine into a set of equations — and why we bother.
Source: course notes, Week 1 foundations.
Before you start
What you need first
- Nothing — this is the very first topic of the course.
- Just everyday experience of things that move: a car, a swing, a robot arm.
What you'll be able to do
- Say what a dynamic model is, in one sentence.
- Tell a static problem from a dynamic one.
- Name the input and output of a model.
- Explain why engineers build models.
What is a dynamic model?
A dynamic model is a set of equations that predicts how a system changes over time.
Static vs dynamic
- Static = frozen. "How much does the shelf bend under a book?"
- Dynamic = moving in time. "How does it wobble after I tap it?"
Everyday examples
- A car bouncing after a speed bump.
- A phone buzzing on a table.
- A robot arm settling after it stops.
Give the model a starting state and an input, and it tells you the
motion that follows.
A model turns an input into a motion
The model is the machine that turns an input into a predicted motion.
| System | Input | Output |
|---|---|---|
| Spring & block | a push | back-and-forth wobble |
| Pendulum | release angle | swinging |
| Robot joint | motor torque | how the arm moves |
Why do we build a model?
| Reason | What it gives you |
|---|---|
| Predict | Know the motion before building or testing. |
| Understand | See why it is fast, slow, or wobbly. |
| Design | Choose masses, lengths, motors on purpose. |
| Save cost & risk | Crash the robot on paper, not in the lab. |
This course lives on reason #2: truly understanding the
model — being able to explain every term.
The whole job, in one picture
This course is the orange box: turning a real machine into equations.
Our focus is the middle step — turning a machine into equations by hand. We can read most of the behaviour straight from those equations; solving them on a computer (later) just draws the picture.
Where this course is headed
Every tool we build points at one target — the model of a real robot arm:
$$M(q)\,\ddot q + C(q,\dot q)\,\dot q + G(q) = \tau$$
🔭 Looking ahead: don't worry about what these symbols mean yet —
each one is a whole topic later. For now, just know the course climbs, step by step,
from a single spring to this full robot-arm equation. Today is step one: knowing what a
"model" even is.
✏️ Try it yourself
For each situation, say whether it is a static or a dynamic problem, and if dynamic, name the input and the output:
- How far a bridge sags under a parked truck.
- How a drone tilts and recovers after a gust of wind.
- How a guitar string vibrates after it is plucked.
1. Static — nothing
changes in time; we only want the final sag under a fixed load.
2. Dynamic —
input: the wind gust (a disturbing force); output: the drone's tilt angle over time.
3. Dynamic —
input: the pluck (initial displacement); output: the string's motion (vibration) over time.
Recap — the whole topic on one screen
| Idea | What you own now |
|---|---|
| Dynamic model | Equations that predict how a system changes in time |
| Static vs dynamic | Frozen final answer vs motion that unfolds over time |
| Input → model → output | A force/torque in, a motion-over-time out |
| Why model | Predict, understand, design, save cost & risk |