One interesting problem with shoe

[ValeryOchkov]

I always wonder why, after a walk in the park, some of my shoes remain clean, while others are always smeared with dirt. I videotaped my walk and realized that the reason was a large welt of brown boots. Drops of water flying up can get on the shoes only if they have a certain trajectory, which depends on the initial conditions (Cauchy problem). Now I am trying to create a mathematical model (ODEs) of this process in Mathcad. Who can help me? May be this problem was solved! 

[ValeryOchkov]

Mathcad- sheets of the article

[ValeryOchkov]

A ball on an elastic band

1D model

2D model

[ValeryOchkov]

Pendulum-amphora

[ValeryOchkov]

[ValeryOchkov]

One more pendulum (new type!)

[-MFra-]

Hi,

I have not yet read your request, and in any case you should know that in Italy (especially in Rome) the subject of shoes is very delicate. When in a speech the word "shoes" is present, excluding the reclames in which one speaks of the quality, of comfort and beauty of the object, in certain cases it can also take different colors that goes from the "yellow" to the "black" or even derogatory (it's a sole = not worth anything). Now I wonder what do they do with mathcad?

[ValeryOchkov]

Thanks, MFra,

Can you give me more information about shoes in Rome?

Here or in private letter.

I am preparing a large article on the pendulum. I write in an article that our arms and legs are the most common pendulum, a compound pendulum. I am doing a mathematical model of a man’s leg swing in a shoe in order to calculate the flight of water droplets from the toe and back of the shoe.

[-MFra-]

Hi Valery,

very nice this pendulum. Mine, on shoes, was only a digression on the subject, which arouses the memory of popular idioms, certainly not in academic circles, so don't take them into account.

[ValeryOchkov]

This is tough! Intrigue and not tell until the end

[ValeryOchkov]

Two different center of coordinate (Figure 7.10):

 

[StuartBruff]

I wonder if you have some commercial opportunity here, Valery?  Perhaps suitably amending the welt profile could alter the trajectory of the spray outwards? 

Then offer to sell the concept to a shoe-polish manufacturer! 😈

Cheers,

Stuart

(Does the spray arise from the upward movement of the foot?)

[ValeryOchkov]

>

[ValeryOchkov]

See please the chapter 4 about  pendulum

in this Russian-English book (bilingual book)

Engineering calculation 

and this site

Pendulum with SMath