Computing Trajectories of a More General Linear Projectile

Computes 3D trajectories of a projectile subject to linear drag, a non-uniform gravitational field, constant wind, and atmospheric thinning.

Context

In [1], we studied, in a full 3D context, a projectile subject to linear drag, a non-uniform gravitational field, time-dependent wind, and parameterized atmospheric thinning. In this general context, we applied a perturbation technique to find exact integral solutions to spatially linearized approximations of the resulting nonlinear, coupled, second-order system of ODEs, with physical interpretations of various quantities throughout the paper. In the special case of constant wind, we provided closed-form solutions, extended our analyses considerably, and provided numerical evidence of the quality of our solutions. This code reproduces that numerical evidence.

This code

We provide the following code to reproduce the numerical evidence presented in [1].

1. lpd__subtrajectoryConstantWind.m -- implements Algorithm 1 of [1].
2. lpd__completeTrajectoryConstantWind.m -- implements Algorithm 2 of [1].
3. lpd__numericallySolveConstantWind.m -- numerically solves the original model of [1] using Matlab's stiff ODE solver ode15s.
4. lpd__compare.m -- compares the order 0, expanded, and numerical solutions of the original model of [1] as computed by lpd__completeTrajectoryConstantWind.m and lpd__numericallySolveConstantWind.m.
5. lpd__saveTrajectoryData.m -- saves comparison data generated by lpd__compare.m as .csv files for subsequent use in creating LaTeX figures.
6. lpd__demo.mlx -- reproduces the numerical evidence presented in [1] as a Live Script demonstration.

References

[1] N. Lorenzo, "A More General Linear Projectile Problem", https://arxiv.org/abs/2411.02145