Computer Program for Dog Chasing Rabbit

[corey2014]

Hey all, I am trying to work on my programming skills. I write programs in C, and I am attempting to write a computer algorithm such that for some small t. Let's call it dt we get the position of a dog, and the position of a rabbit, as the dog chases the rabbit. This is being asked on a mathematics portion because its a differential equation. The prototypical Dog chases a rabbit with some velocity greater than the rabbits, and we want to know what path the Dog takes. I have a program written such that all I need is to plug in points and it will graph the path... The only problem I am running into is how to create an algorithm for this... Any and ALL help is appreciated!

I know the analysis equation, and how that would make this much easier, however, being an applied Mathematics type person I want to write a computer script without using that.

 

[Office_Shredder]

The only problem I am running into is how to create an algorithm for this

What exactly is this? Calculating the points of where the rabbit and dog are? When you say you know the analysis equation I don't really know what that means, but I'm unclear on how you're going to calculate where the dog is without some sort of equation.

It would help if you spell out your specific problem with more detail: it sounds like you have a differential equation that you just want to calculate the solution of numerically but I really can't be sure

 

[corey2014]

Consider a rabbit which sits a distance L east of a dog. At time t = 0 the rabbit
starts running north (in y-direction) at constant speed v. The dog starts chasing the
rabbit at constant speed 2v, and always changes its running direction towards the
rabbit. The rabbit always runs north and never changes direction.

Basically I want a program that goes toward the rabbit other than the easy y=2/3*L{1-(x/2L+1)*sqrt(1-x/L)} and I understand it will never become zero... But I want to simulate this...

 

[Office_Shredder]

If you have the current position of the rabbit and of the dog, there are two steps

1 calculate the velocity of the dog

2 assume some small time 1/100 if a second say, had passed and add 1/100th of the signs velocity to his position, and similarly for the rabbit

 

[blue_raver22]

I would first like to commend you on your efforts to improve your programming skills and your interest in applying mathematics to solve real-world problems. The task of creating a computer program for dog chasing rabbit is indeed a challenging one, but with the right approach and tools, it is definitely achievable.

One approach you could take is to break down the problem into smaller steps. First, you would need to define the initial positions and velocities of the dog and rabbit. Then, you could use a loop to simulate the movement of the dog and rabbit over small time intervals (dt). Within this loop, you could use mathematical equations to calculate the new positions of the dog and rabbit at each time step.

To determine the path of the dog, you could use the concept of vectors to represent the direction and magnitude of the dog's velocity. You could also consider factors such as the dog's agility and the rabbit's movements to make the simulation more realistic.

In terms of the algorithm, you could use conditional statements to determine when the dog catches the rabbit or when the rabbit escapes. Additionally, you could include a stopping condition to end the simulation once the dog and rabbit have reached a certain distance from each other.

It is also important to continuously test and debug your program to ensure its accuracy and efficiency. You could also consider incorporating visualizations or animations to make the program more interactive and user-friendly.

Overall, creating a computer program for dog chasing rabbit requires a combination of mathematical knowledge, programming skills, and problem-solving abilities. With persistence and determination, I have no doubt that you will be able to successfully create an algorithm and program for this scenario. Good luck!