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Wolf and hare - one old problem with simple Mathcad solution

ValeryOchkov
Ruby I

Wolf and hare - one old problem with simple Mathcad solution

WolfHare.gif

27 REPLIES 27

Re: Wolf and hare - one old problem with simple Mathcad solution

Hi 

Very beautiful. I also have the analytical solution.

Re: Wolf and hare - one old problem with simple Mathcad solution

Show please!
But the solution without animation is not solution!

Re: Wolf and hare - one old problem with simple Mathcad solution

Hi

I only provide you with the most important part I have developed. Let me know if you find something wrong. (After the formula (11) there is still some simple calculation to do)
Greetings FM.

Greyhound-hare tracking curve.jpg

Greyhound-hare tracking curve 1.jpg

Re: Wolf and hare - one old problem with simple Mathcad solution

Thanks!

But show please the analytical view of the wolf (or борзая) tracing curve!

One Russian article with the formula is here

PS Greyhound (русская псовая борзая) is the only breed of dogs that is bred in Russia:

grayhound.png

 

Re: Wolf and hare - one old problem with simple Mathcad solution

Hi ValeryOchkov,

thank you very much for the article on the topic under consideration. 

 

Re: Wolf and hare - one old problem with simple Mathcad solution

… but this problem has no analytical solution

WolfHare-Square.gif

 

Re: Wolf and hare - one old problem with simple Mathcad solution

and one more

WolfHare-Circle-1.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

… one more

WolfHare-90.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

… and one more

WolfHare-Ellipse.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

The wolf must stay and wait for the hare...

WolfHare-Circle-3.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

… and one more

WolfHare-Spiral_1.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

WolfHare-Square-1.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

Very simple solution

Solution.png

Re: Wolf and hare - one old problem with simple Mathcad solution

One interesting problem for an analytical solution - what is the formula of this closed curve?

WolfHare-Spiral.png

Re: Wolf and hare - one old problem with simple Mathcad solution

 

WolfHare-Circle-1-3.gifWolfHare-Circle-1-4.gifWolfHare-Circle-1-5.gif

Re: Wolf and hare - one old problem with simple Mathcad solution


here@-MFra- wrote:

Hi ValeryOchkov,

thank you very much for the article on the topic under consideration. 

 


You welcome!

See please one English article here

And my article in attach (Russian)

And of course Pursuit curve

Re: Wolf and hare - one old problem with simple Mathcad solution

I look and look at this animation and I expect that the hare will still run away from the wolf into the forest...

Re: Wolf and hare - one old problem with simple Mathcad solution


@ValeryOchkov wrote:
I look and look at this animation and I expect that the hare will still run away from the wolf into the forest...

The hare has an afterburner. The hare turns it on when the distance to the wolf becomes less than 300 m. Therefore, the hare can be saved in the forest from the wolf!

Can you solve this problem analytical?

And the second (new, fresh) problem! The hare does not run in a straight line, but along a circular arc!

WolfHare-Forsage.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

One symbolic solution one partial case of the problem

WolfHareSymbol.png

 

Re: Wolf and hare - one old problem with simple Mathcad solution

The DE of the problem. See Pursuit curve

Wolf-Hare-ODE.png

Re: Wolf and hare - one old problem with simple Mathcad solution

Dog -> Wolf -> Hare (see alse Mice problem)

WolfHareDog.gif

Re: Wolf and hare - one old problem with simple Mathcad solution


@ValeryOchkov wrote:

The DE of the problem. See Pursuit curve

Wolf-Hare-ODE.png


 There is an error on Wikipedia - not (a-x^2) but (a-x)^2

ddy.png

 

Re: Wolf and hare - one old problem with simple Mathcad solution

3D

HawkHare.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

The hawk chased the hare, landed, and ... drove out of the runway. Fog!

HawkHare-Fog.gif

Re: Wolf and hare - one old problem with simple Mathcad solution

Re: Wolf and hare - one old problem with simple Mathcad solution

Correct variant in attach!

Wolf-Hare.png

Re: Wolf and hare - one old problem with simple Mathcad solution

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