Mathematics of Classical Mechanics
The mechanics of rigid bodies which I learned in engineering classes was mostly:
- Draw a system.
- Draw a lot of forces and constraints.
- Select a coordinate system. Mostly XYZ.
- Calculate. When something strange happen, check your forces again.
Using this approach for moving parts was pretty annoying.
I will use a couple of books.
- [Structure and Interpretation of Classical Mechanics].
- PRO: Is it is publicly available
- PRO: It use programming for experiments.
- PRO: The authors care about didactics.
- PRO: Operator notation. D_1(f) instead of df/dx (I need mathematical notation here)
- CON: They use an old version of Scheme which you need to install first.
- Mathematical Methods of Classical Mechanics Second Edition, V.I. Arnold. I prefer the Russian Version. There are are also translations to German and English
- PRO: More mathematical formalism.
- CON: I feel that I miss some mathematical and physical knowledge to understand it. Example: I did not know additive groups of type AxB->C and did not work a lot with affine spaces.
- Курс теоретической физики Ландау и Лифшица (Course of Theoretical Physics from L. Landau and E. Lifshitz), Volume 1, Mechanics. 
- PRO: More physics.
- PRO: Good quality, as a classical teaching book in Soviet Union.
- CON: Too sloppy mathematical formalism for me. Too view intermediate steps.
System of coordinates
Image we want to describe a two dimensional motion of a printing head in X-Y plane. For simplicity, we ignore the Z axis. It does not matter how want measure the position of the head. The printer will work always in the same way.
(Add picture with cartesian, radial and moving coordinates here.)
Here we test mathematical formulas. <math>