This section covers techniques for handling numerical challenges in rocket simulation.
Topics¶
- Singularity Guards - Handling \(1/v\) and \(1/r\) problems
Overview¶
The equations of motion contain terms that can become singular:
\[
\frac{d\gamma}{dt} = \frac{T}{mv}\sin\alpha + \left(\frac{v}{r} - \frac{\mu}{r^2 v}\right)\cos\gamma
\]
Both \(1/v\) and \(1/r\) can cause numerical issues.
Key Techniques¶
- Regularization: Replace singular terms with smooth approximations
- Guarding: Clamp values to safe ranges
- Filtering: Remove non-physical trajectory points