SICM Exercise 1.02

Solution to exercise 1.2 of Structure and Interpretation of Classical Mechanics by Gerald Jay Sussman and Jack Wisdom.

Generalized coordinates

🛈 Note

For each of the systems in exercise 1.1 , specify a system of generalized coordinates that can be used to describe the behavior of the system.

1. One tuple for each juggling pin. Each tuple contains two other tuples: one for specifying the position in carthesian coordinates (three variables) and one for specifying the orientation (three variables).
2. One tuple for describing the rotation around two axes.
3. A tuble containing two other tuples tuples, which are the same as the tuple in the previous example.
4. A tuple containing a single variable which measures the distance from the beginning of the wire.
5. A tuple containing two variables, which specify the orientation. Since we have only two axes of rotation we need only two variables.
6. A tuple conatining the three variables, which specify the orientation. Now we have three axes of rotation.