Page:Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/264

Variations annuelles des plus grandes équations.

${\begin{aligned}{\frac {2d\lambda \ \ \ }{dt}}=&-1''{,}1060m',\\{\frac {2d\lambda '\ \ }{dt}}=&0''{,}5628m-0''{,}0002m'',\\{\frac {2d\lambda ''\ }{dt}}=&0{,}0130m+0''{,}3168m'+0''{,}0366m'''+0''{,}0022m^{\scriptscriptstyle {\text{IV}}}+0''{,}0022m^{\scriptscriptstyle {\text{V}}},\\{\frac {2d\lambda '''}{dt}}=&-0''{,}0008m-0''{,}1602m'-0''{,}0494m''+0''{,}0418m^{\scriptscriptstyle {\text{IV}}}-0''{,}0080m^{\scriptscriptstyle {\text{V}}},\\{\frac {2d\lambda ^{\scriptscriptstyle {\text{IV}}}}{dt}}=&-0''{,}0014m-0''{,}0616m'-0''{,}0064m''-0''{,}0902m'''-0''{,}0902m^{\scriptscriptstyle {\text{V}}},\\{\frac {2d\lambda ^{\scriptscriptstyle {\text{V}}}\ }{dt}}=&0''{,}0002m-0''{,}0126m'-0''{,}0022m''+0''{,}0058m'''+0''{,}0304m^{\scriptscriptstyle {\text{IV}}}.\end{aligned}}$

Mouvements annuels des nœuds sur l’écliptique vraie.

${\begin{aligned}{\frac {d\Omega \ \ \ }{dt}}=&-0''{,}3403m-12''{,}2792m'-0''{,}1422m''-0''{,}0010m'''-8''{,}0564m^{\scriptscriptstyle {\text{IV}}}\\&-0''{,}1095m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\Omega '\ \ }{dt}}=&5''{,}8758m-6''{,}9480m'-0''{,}3894m''-0''{,}0089m'''-17''{,}5615m^{\scriptscriptstyle {\text{IV}}}\\&-0''{,}3128m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\Omega ''\ }{dt}}=&-0''{,}4674m-11''{,}0018m'-0''{,}4330m''-1''{,}7724m'''-11''{,}7980m^{\scriptscriptstyle {\text{IV}}}\\&-0''{,}3187m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\Omega ^{\scriptscriptstyle {\text{IV}}}}{dt}}=&-0''{,}2856m-5''{,}1352m'-0''{,}2872m''-6''{,}6908m'''-7''{,}4579m^{\scriptscriptstyle {\text{IV}}}\\&+0''{,}1640m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\Omega ^{\scriptscriptstyle {\text{V}}}\ }{dt}}=&-0''{,}1176m-2''{,}1843m'-0''{,}1431m''-0''{,}8696m'''-5''{,}5698m^{\scriptscriptstyle {\text{IV}}}\\&-0''{,}0976m^{\scriptscriptstyle {\text{V}}}.\end{aligned}}$