Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.02145 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917828062347264 |
|---|---|
| author | Lorenzo, Nick |
| author_facet | Lorenzo, Nick |
| contents | In a full 3D context, we study a projectile subject to linear drag, a non-uniform gravitational field, time-dependent wind, and parameterized atmospheric thinning. In this general context, we provide integral solutions, exact to $\mathcal{ O }( \varepsilon )$, for the position and velocity of the projectile, where $\varepsilon$ is a small perturbation parameter; in the special case of constant wind, we provide closed-form solutions, exact to $\mathcal{ O }( \varepsilon )$. Under the constant-wind assumption, we provide closed-form solutions of $\mathcal{ O }( 1 )$ for the time of tangency, times of flight, and extreme values of the radius achieved by the projectile. We provide physical interpretations throughout, including a physical interpretation of the branches $W_0$ and $W_{ -1 }$ of the Lambert W function in the context of flight time. We also provide parameterized, error-controlled algorithms to compute trajectories, complete with a full Matlab implementation that we make freely available. We compare the results of our implementation to a general-purpose, stiff ODE solver. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A More General Linear Projectile Problem Lorenzo, Nick Classical Physics In a full 3D context, we study a projectile subject to linear drag, a non-uniform gravitational field, time-dependent wind, and parameterized atmospheric thinning. In this general context, we provide integral solutions, exact to $\mathcal{ O }( \varepsilon )$, for the position and velocity of the projectile, where $\varepsilon$ is a small perturbation parameter; in the special case of constant wind, we provide closed-form solutions, exact to $\mathcal{ O }( \varepsilon )$. Under the constant-wind assumption, we provide closed-form solutions of $\mathcal{ O }( 1 )$ for the time of tangency, times of flight, and extreme values of the radius achieved by the projectile. We provide physical interpretations throughout, including a physical interpretation of the branches $W_0$ and $W_{ -1 }$ of the Lambert W function in the context of flight time. We also provide parameterized, error-controlled algorithms to compute trajectories, complete with a full Matlab implementation that we make freely available. We compare the results of our implementation to a general-purpose, stiff ODE solver. |
| title | A More General Linear Projectile Problem |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2411.02145 |