1.3: Text structure
In this textbook, the techniques and models that scientists and engineers need to design and analyse dynamical systems will be introduced step by step, starting from Newton’s laws. Eventually at the end of the textbook we will have discussed a toolbox of equations and techniques that can be valuable for your future career.
The text consists of different parts:
- Descriptions and explanations
- Derivations of key equations and concepts
- Concepts and techniques in dynamics
- Practical examples, and sample problems that illustrate the use of these techniques
Although derivations of equations might be skipped without following the main line of the textbook, it is highly recommended to read them, since they do provide more insight into the theory and demonstrate beautifully how Newton’s laws, despite their simplicity, can account for a tremendous set of complex phenomena in dynamics.
To highlight important concepts, they are introduced like this:
\[\sum_{j} m_{j} \overrightarrow{\boldsymbol{v}}_{j}\left(t_{1}\right)+\sum_{i, j} \int_{t_{1}}^{t_{2}} \overrightarrow{\boldsymbol{F}}_{i, j} \mathrm{~d} t=\sum_{j} m_{j} \overrightarrow{\boldsymbol{v}}_{j}\left(t_{2}\right) \tag{1.1} \label{1.1}\]
Similarly, derivations are marked like this:
Examples to illustrate how to apply the concepts and techniques are provided in an example environment, with the letter in front of the example indicating the difficulty level (S: simple, M: medium and A: advanced).
We consider the following example situation.
Exemplary solution
The dynamics of this system can be solved as follows.
Problems are included in these notes as follows:
| M Problem 1.1 This is a test problem.