Speakur

Word Pronunciation & Dictionary

liouville-arnold theorem

Word Rarity Very rare

Frequency: Zipf frequency 1.80 in modern English

Syllables
li-ou-ville-arnold the-o-rem
IPA
31
Scrabble Score
22
Letters
6
Syllables
13
Unique Chars

Meaning

name

In dynamical systems theory, a theorem stating that if, in a Hamiltonian dynamical system with n degrees of freedom, there are also known n first integrals of motion that are independent and in involution, then there exists a canonical transformation to action-angle coordinates in which the transformed Hamiltonian is dependent only upon the action coordinates and the angle coordinates evolve linearly in time. Thus the equations of motion for the system can be solved in quadratures if the canonical transform is explicitly known.

Etymology

Named after Joseph Liouville and Vladimir Arnold.

Inflected Forms

the Liouville-Arnold theorem (canonical)

Questions

What does liouville-arnold theorem mean?
In dynamical systems theory, a theorem stating that if, in a Hamiltonian dynamical system with n degrees of freedom, there are also known n first integrals of motion that are independent and in involution, then there exists a canonical transformation to action-angle coordinates in which the transformed Hamiltonian is dependent only upon the action coordinates and the angle coordinates evolve linearly in time. Thus the equations of motion for the system can be solved in quadratures if the canonical transform is explicitly known.
Where does liouville-arnold theorem come from?
Named after Joseph Liouville and Vladimir Arnold.

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