Lagrange Points Derivations | Orbital Mechanics with Python 55 скачать в хорошем качестве

Lagrange Points Derivations | Orbital Mechanics with Python 55

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). Instagram and TikTok: @spaceengineeringpodcast   / spaceengineeringpodcast     / spaceengineeringpodcast   #lagrangepoints #astrodynamics #python