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検索結果- 英語 - 多言語
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Liouville-Arnold theorem
固有名詞
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.
日本語の意味
リウヴィル・アーノルドの定理とは、力学系理論において、n自由度のハミルトン系で、独立かつ可換なn個の第一積分が存在する場合に、正準変換を用いて作用角座標系に変換できることを示す定理です。変換後のハミルトニアンが作用座標のみに依存し、角座標が時間に対して線形に進むため、運動方程式が積分可能になるという主張がなされています。
英語の意味
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.
関連語
