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V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
October 10, 2018
Question

Mice problem

  • October 10, 2018
  • 3 replies
  • 6893 views

See please here Mice problem about this task!

You can see in attach a Mathcad 15 file with solution of this problem.

But I think that will be better to use not a X-Y system but a Polar system of coordinate - for the calculation and for the plotting - not only for 4 animals but for 3, 5, 6 etc. Help me please!

4-Hare.gif 

3 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
October 13, 2018

3D variant - not mice but bats!

4-Flyer.gif

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
October 14, 2018

3D animation without three 2D animations is not an animation!

4-Flyer-ZX.gif4-Flyer-YX.gif4-Flyer-ZY.gif

 

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
November 27, 2018

Sorry - it is not bats but bugs problem! But for me bugs are not 3D but 2D animals!

 

  • Arnold M., Zharnitsky V. Cyclic evasion in the three bugs problem //American Mathematical Monthly. 2015. Vol. 12, issue 4. Pp. 377-380. URL: https://doi.org/10.4169/amer.math.monthly.122.04.377
  • Chapman S., Lottes J., Trefethen L. Four bugs on a rectangle // Proc. of The Royal Society A. 2011. Vol. 467(2127). Pp. 881–896. DOI: 10.1098/rspa.2010.0506
A
AlvaroDíaz12-Amethyst
12-Amethyst
November 28, 2018

Hi Valery. Try this, using complex numbers.

Best regards.

Alvaro.

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    November 28, 2018
    @AlvaroDíaz wrote:

    Hi Valery. Try this, using complex numbers.

    Best regards.

    Alvaro.

    Thanks Alvaro - its very interesting!

    And what about a 3D problem - a bugs/bats problem with complex numbers?

    A
    AlvaroDíaz12-Amethyst
    12-Amethyst
    November 29, 2018

    Hi Valery. Sorry, but one of my old complex variable books have a lot of examples of applications in 2D of complexes: fluids, mechanical systems, thermal systems ... but nothing about 3D, so I assume that there are not way to cover with complexes that. I loose that book and can't remember the author. So, maybe only with quaternions you can improve the speed and get more elegant equations, but it imply a lot of work.

     

    Best regards.

    Alvaro.

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