Élimination du temps et équation différentielle des trajectoires dans le problème des trois corps restreint, circulaire, plan
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1972
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Hours (Time) Problem of three bodies Duración Horas (Tiempo) Décret Circulaire Arrêté Texte Réglementaire Loi Problème des trois corps Trois corps, Problème des 3 corps, Problème desCiter ce document
Anne Sergysels-Lamy et al., « Élimination du temps et équation différentielle des trajectoires dans le problème des trois corps restreint, circulaire, plan », Bulletins de l'Académie Royale de Belgique, ID : 10.3406/barb.1972.60470
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It is well known that the system of differential equations of motion in the circular, planar, restricted problem of three bodies can be reduced to the second order, using the Jacobian integral to eliminate time. However, the differential equation of trajectories, so obtained, is extremely complex and is of no practical use. But, in the case of weakly perturbed Keplerian motion and not using the Jacobian integral to eliminate time, the differential equation of trajectories has a form that makes possible its study by known methods of nonlinear mechanics.