Gradient of CR3BP Gravitational Pseudo-Potential Function | Orbital Mechanics with Python 53
In this video we go over the circular restricted 3 body problem pseudo-potential function, how to calculate its gradient (vector of partial derivatives) with respect to the position vector which we’ll use for our second order differential equation to be able to propagate trajectories in this rotating reference frame. And is how it is plugged into the CR3BP class differential equation method in the GitHub repository. Also note that when the gradient of the pseudo-potential function equals 0, it is a lagrange point!
We start by going over the two-body acceleration gravitational potential function in order to give more familiar context for what the circular restricted 3 body problem pseudo-potential function is.
The CR3BP gravitational pseudo-potential function is equal to the gravitational potential from the first body plus gravitational potential of the second plus a term for the rotating reference frame.
#3bodyproblem #threebodyproblem #multivariablecalculus
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