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  "body": "\n## Summary\n\nAn integrable system is a [[Hamiltonian system|0EDKGA2FAK]] with as many independent conserved quantities in involution as it has degrees of freedom.\nSuch a system can be solved, in principle, by quadratures, and its motions on compact regular level sets are quasi-periodic motions on invariant tori.\nThe word is also used for infinite-dimensional systems, such as the Korteweg–De Vries equation.\nThese have infinitely many conserved quantities and can be solved by inverse scattering.\nIntegrable systems are the starting point of perturbation theory, where the question is what survives when the system is slightly changed.\n\n## Explanations\n\n### L1 human\n\nMost mechanical systems cannot be solved by a formula, but integrable ones can.\nThey have enough conserved quantities, like energy and angular momentum, to pin down each motion.\nPicture each motion as winding around the surface of a doughnut, at fixed speeds in each direction.\nTwo independent harmonic oscillators are integrable: the energy of each oscillator is conserved, and each one simply turns around a circle.\n",
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