Program calculating bounces of a particle off circles.

In summary, the goal of this exercise is to shoot a particle at 3 circles in an equilateral triangle, with a side length of 6 units and circle radius of 1 unit, and have it bounce around and eventually escape without creating an infinite number of bounces. The asker has written a computer program to model this behavior and is asking for suggestions on the starting location and angle to achieve the highest number of hits. Another user has suggested starting with a trajectory that would generate infinite bounces and making small modifications to achieve arbitrarily high numbers of bounces.
  • #1
firegoalie33
3
0

Homework Statement


Okay. So my goal is to bounce a particle off of 3 circles with centers at the vertices of an equilateral triangle. The side length of each side of the triangle is 6 units and the radius of the circles are 1 unit. I am shooting a particle from anywhere at any angle with unit speed. The particle needs to bounce around in the system of circles and eventually escape. I have written a computer program to model this behavior. I am NOT allowed to shoot it in a manner that creates an infinite number of bounces.


Homework Equations



Does anyone have a hunch as to what starting location and starting angle i should use to get the highest number of hits?


The Attempt at a Solution



The most i can get is three. and this was done using random numbers in the computer.
 
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  • #2
If there actually exists an analytic way to get an infinite number of bounces, I would suspect that you can also achieve any arbitrarily high number of bounces depending on your machine accuracy.

I.e. If some trajectory yields an infinite number of bounces, then a tiny perturbation from that trajectory should yield a very large number of bounces, and progressively smaller perturbations will yield arbitrarily high numbers of bounces.
 
  • #3
I am with zhermes here - start with shot that should generate infinite bounces, modify the angle by any amount - the smaller the better.
 

Related to Program calculating bounces of a particle off circles.

1. What is the purpose of a program that calculates bounces of a particle off circles?

The purpose of this program is to simulate the movement of a particle bouncing off circular objects, such as walls or obstacles, in a controlled environment. This can be used to study the behavior of the particle and its interaction with the circles, and can have practical applications in fields such as physics, engineering, and computer graphics.

2. How does the program calculate the bounces of a particle off circles?

The program uses mathematical equations and algorithms to determine the trajectory of the particle as it bounces off the circles. It takes into account the position, velocity, and other characteristics of the particle, as well as the size and location of the circles, to accurately calculate the bounces.

3. What are the inputs required for the program to calculate bounces?

The program typically requires inputs such as the initial position and velocity of the particle, the size and location of the circles, and any other relevant parameters such as the coefficient of restitution or the gravitational force. These inputs can vary depending on the specific implementation of the program.

4. Can the program account for different types of collisions?

Yes, the program can be designed to handle different types of collisions, such as elastic or inelastic collisions. This can be achieved by adjusting the mathematical equations or adding additional parameters to the program.

5. Are there any limitations to the accuracy of the program?

Like any simulation, the accuracy of the program depends on the quality of the inputs and the complexity of the system being simulated. Small errors in the inputs or simplifications in the equations can lead to deviations from real-world behavior. Additionally, the program may not be able to account for external factors such as air resistance or friction, which can affect the movement of the particle.

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