Translation of "Lagrange" to Russian language:
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| Lagrange solved this problem in 1755 and sent the solution to Euler. | Лагранж решил эту задачу в 1755 году и отослал решение Эйлеру. |
| Note that formula_108This has the form of formula_109(where we have performed a change of dummy indices) so set formula_110Then, formula_111 formula_112Noether's theorem states that formula_113 (as one may explicitly check by substituting the Euler Lagrange equations into the left hand side). | Note that formula_141This has the form of formula_142(where we have performed a change of dummy indices) so we can set formula_143Then, formula_144 formula_145Noether s theorem states that formula_146 (as one may explicitly check by substituting the Euler Lagrange equations into the left hand side). |
| The barycenter being both the center of mass and center of rotation of the three body system, this resultant force is exactly that required to keep the smaller body at the Lagrange point in orbital equilibrium with the other two larger bodies of system. | Так как центр масс является одновременно и центром вращения системы, результирующая сила точно соответствует той, которая нужна для удержания тела в точке Лагранжа в орбитальном равновесии с остальной системой. |
