Increase order of subtimestep propagation inside collisions

[gomezzz]

Feature

Desired behavior

Better accuracy through higher interpolation order inside the collision detection here

LADDS/src/ladds/CollisionFunctor.cpp

Line 59 in 42ace8a

// if distance is smaller we compute the minimum distance between the linear interpolations

Currently only linear but have noted that we get different conjunctions for different time step sizes. This should hopefully change that.

What needs to be done

• Find a polynomial or similar to cheaply approximate trajectory where ideally intersection of the two polynomials is also cheap.
• Compute / Store in-between positions of particles (this relies on the integrator as well. current Yoshida integrator may be suboptimal here)
• In CollisionFunctor (analytically) compute distance between interpolated trajectories

How it can be tested

• Run compare to linear
• Run different timesteps over 1 year to see if results are more deterministic.