Lagrange Points Derivations | Orbital Mechanics with Python 55

Опубликовано: 15 Январь 2022
на канале: Alfonso Gonzalez - Astrodynamics & SE Podcast

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In this video we go over the derivation of the 5 Lagrange points in the CR3BP which occur when the gradient of the pseudo-potential function omega is equal to zero. We start with the co-linear solutions where the y and z position components are equal to zero from which we need a root solver to converge on the resulting x coordinates of L1, L2 and L3.

Then move onto the triangular solutions L4 and L5, where we linearize the two equations with 2 unknowns to be able to solve for the norm of the position vectors with a matrix-vector method, which tells us that the solutions form an equilateral triangle with the 2 bodies (L4 and L5).

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