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.

But maybe there is a more elegant way to do it? I hope to use a more mathematical approach, like Langrangian and Hamiltonian mechanics.

Books

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. [1]
  • 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

(Under construction)

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.)