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 demonstration and experinats.
* PRO: The authors care about didactitics.
* 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 mathematics and physics knowledge to understand it.

• 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.