About 1 Dimensional 3-body problem

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In summary, the conversation discusses the release of three positively charged particles in a 1-dimensional space and the use of known interaction potentials to determine their final velocities when they are far apart. It is noted that without additional information or assumptions, dynamic equations would need to be used to study the time evolution of the system.
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cracking
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hi all,
Suppose three charged particles (all positive) m1,q1; m2,q2; m3,q3 are released and can move only in 1 dimension say x-axis and their interaction potential are known (say q1q2/(x1-x2)2). When they very far from one another (i.e. all potential released), are there formulas which can give their final velocities?
Suppose no symmetric configurations are there, then I notice that the momentum (1-D ) and energy conservation only give 2 equations for three velocities. Do I have no choice except use dynamic equations to study their time evolution?
 
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  • #2
Yes, you are correct. Without some additional information or assumptions about the system, you would need to use dynamic equations to study the time evolution of the system. You may also be able to make some assumptions about the initial configuration or velocities of the particles in order to solve for the final velocities.
 

FAQ: About 1 Dimensional 3-body problem

What is the 1 Dimensional 3-body problem?

The 1 Dimensional 3-body problem is a classic problem in physics and astronomy that involves studying the motion of three objects (usually stars or planets) that are interacting with each other through gravitational forces. It is called "1 dimensional" because the objects are all confined to a single line or plane, and "3-body" because there are three objects involved.

Why is the 1 Dimensional 3-body problem significant?

The 1 Dimensional 3-body problem is significant because it serves as a simplified model for understanding more complex systems, such as the interactions between multiple stars or planets in space. It also has real-world applications in fields such as celestial mechanics and astrodynamics.

What are the key equations used to solve the 1 Dimensional 3-body problem?

The key equations used in solving the 1 Dimensional 3-body problem are Newton's laws of motion and the law of universal gravitation. These equations describe how objects move and interact with each other due to gravitational forces.

What are some challenges in solving the 1 Dimensional 3-body problem?

One of the main challenges in solving the 1 Dimensional 3-body problem is that there is no general analytical solution for all possible initial conditions. This means that specific numerical methods must be used to approximate the motion of the objects over time. Additionally, the problem becomes increasingly complex as more objects are added, making it difficult to find exact solutions.

How is the 1 Dimensional 3-body problem related to chaos theory?

The 1 Dimensional 3-body problem is closely related to chaos theory, which studies the behavior of dynamic systems that are highly sensitive to initial conditions. Due to the complex and unpredictable nature of the interactions between three objects, the 1 Dimensional 3-body problem can exhibit chaotic behavior, making it a subject of interest for chaos theory researchers.

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