Exploring Periodic Distribution of Rigid Balls in a Vast Space

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Homework Help Overview

The discussion revolves around the behavior of rigid balls in a vast space, particularly focusing on their interactions with spherical springs arranged in a tetrahedral configuration. The original poster seeks to understand if there is a periodic distribution of density or energy density resulting from these interactions, akin to diffraction patterns in light. The problem is set in an idealized environment without gravity, emphasizing the need for a functional relationship among unknown variables.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants inquire about the nature of the spherical springs, questioning whether they actively contribute energy to the system or remain passive. There are discussions about the implications of changing the number of springs and the relevance of existing physical models to the problem. Some participants express uncertainty about the terminology used, such as "positive tetrahedron," and seek clarification on the original poster's intent.

Discussion Status

The conversation is ongoing, with participants actively seeking clarification on the original poster's statements and exploring various interpretations of the problem. There is a notable emphasis on understanding the assumptions and definitions involved, particularly regarding the behavior of the spherical springs and the configuration of the rigid balls.

Contextual Notes

Participants have noted the potential for changing conditions within the problem, such as the number of spherical springs and their motion. The original poster has indicated a desire to simplify the problem initially before addressing more complex scenarios. There is also a mention of translation challenges affecting communication.

crazy lee
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Homework Statement
ball collision
Relevant Equations
don't know
First of all, all the physical quantities presented in this topic are unknown variables, and I require a functional relationship between these unknown variables.

In a vast space that does not consider gravity , there are many ideal rigid balls moving freely. And in equilibrium. The ball is very hard and there is no energy loss in the collision. Now place four spherical springs in it. The four spherical springs are on the four vertices of the positive tetrahedron. The spherical spring retracts repeatedly.

Question: Is there a periodic distribution of density or energy density in space for a rigid ball after repeated impact by a spherical spring? Notice the periodic distribution in space, just like the diffraction interference fringes of light. That is, in some places in space, where the density of a rigid ball is always greater than that of other places.

Conditions can change in the middle of this problem. For example, change the number of spherical springs to five. The relative position and motion state of the spherical spring can be adjusted at will. Be careful with existing ideal physical models. Because the methods summarized from the ideal model may not hold true in current problems.

my english is bad. thank you
 
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crazy lee said:
Homework Statement:: ball collision
Relevant Equations:: don't know

Be careful with existing ideal physical models
Can you specifically reference an existing model please?
 
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hutchphd said:
Can you specifically reference an existing model please?
thank you.For example, I don't know if laws and formulas derived from the propagation of sound waves also hold true on this issue。
 
I rely on translation software to communicate with

you, because I really want to know the answer to the

question
 
Where can I read about "existing ideal physical models" that you talk about, Point out one or two references please.
 
crazy lee said:
positive tetrahedron
What is a "positive tetrahedron"?
crazy lee said:
The spherical spring retracts repeatedly.
This is not clear to me. Are there four spheres putting energy into the system by expanding and contracting as the balls bounce off them?
Or are they passive, acting just like the bouncing balls except that they are fixed in position?
The question sounds like it is asking whether you can get standing waves, which suggests they're passive.
crazy lee said:
Conditions can change in the middle of this problem. For example, change the number of spherical springs to five.
Is this saying that more of these spheres can pop into existence dynamically, or that you need to answer the question for (constant) N spheres, not just 4?
Either way, not a tetrahedron now, obviously, so what instead?
 
Last edited:
hutchphd said:
Where can I read about "existing ideal physical models" that you talk about, Point out one or two references please.
------------------
I haven't read any ideal model related to my problem. I say this because someone studied a lot of ideal rigid balls directly as air before. I don't think so
 
haruspex said:
What is a "positive tetrahedron"?
--------------------------------------------
positive tetrahedron is Regular tetrahedron.Problems with translation software
haruspex said:
This is not clear to me. Are there four spheres putting energy into the system by expanding and contracting as the balls bounce off them?
Or are they passive, acting just like the bouncing balls except that they are fixed in position?
The question sounds like it is asking whether you can get standing waves, which suggests they're passive.
------------------------------------------
Four spheres does not absorb or release energy.You can think that their motion is active, but they can adjust the motion parameters so that they do not release or absorb energy. The fixed position is to simplify the problem. Finally, I will cancel this restriction so that the spherical spring can move freely。It's a bit like standing wave, but I'm not sure if I can study a rigid ball as air. The motion of the spherical spring is indeed passive, but I cannot explain how the spherical spring can be retracted repeatedly in passive motion.

haruspex said:
Is this saying that more of these spheres can pop into existence dynamically, or that you need to answer the question for (constant) N spheres, not just 4?
Either way, not a tetrahedron now, obviously, so what instead?
---------------------------------------------
My idea is to try to simplify the problem first. See if the simplified problem can be solved. Once the simplified problem can be solved, all conditions can be relaxed

thank you very much.
 

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