Exploring Periodic Distribution of Rigid Balls in a Vast Space

[crazy lee]

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

 

[hutchphd]

Homework Statement:: ball collision
Relevant Equations:: don't know

Be careful with existing ideal physical models

Can you specifically reference an existing model please?

 

[crazy lee]

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。

 

[crazy lee]

I rely on translation software to communicate with

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

question

 

[hutchphd]

Where can I read about "existing ideal physical models" that you talk about, Point out one or two references please.

 

[haruspex]

positive tetrahedron

What is a "positive tetrahedron"?

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.

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?

 

[crazy lee]

Where can I read about "existing ideal physical models" that you talk about, Point out one or two references please.

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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

 

[crazy lee]

What is a "positive tetrahedron"?
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positive tetrahedron is Regular tetrahedron.Problems with translation software

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.
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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.

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?

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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.