What is the Three-Body Problem in Physics and Why is it Considered Unsolvable?

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SUMMARY

The Three-Body Problem in physics is a classic example of an ordinary differential equation (ODE) that remains unsolvable analytically in its general form. While specific solutions exist for particular configurations, a comprehensive solution applicable to all scenarios has not been achieved. This problem exemplifies the complexities of classical mechanics and highlights the limitations of analytical methods in solving certain physical systems.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with classical mechanics concepts
  • Basic knowledge of analytical methods in physics
  • Awareness of specific examples like pendulums and coupled springs
NEXT STEPS
  • Research the specific conditions under which the Three-Body Problem can be solved
  • Explore numerical methods for approximating solutions to unsolvable ODEs
  • Study the implications of chaotic systems in classical mechanics
  • Investigate other unsolvable ODEs in physics beyond the Three-Body Problem
USEFUL FOR

This discussion is beneficial for physics students, researchers in classical mechanics, and anyone interested in the complexities of dynamical systems and their mathematical challenges.

dipole
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Hi, I'm trying to come up with some examples of ODEs (not PDES) in physics that are unsolvable analytically, and for some reason I'm drawing a blank.

There are a few obvious examples from classical mechanics such as a pendulum and coupled springs etc... but beyond that I can't seem to recall coming across any.

Can anyone think of some ODEs that describe interesting physics and whose derivation can be understood without too much background knowledge?
 
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