IM1: Simple Point Mass¶
Inputs¶
- \(\rho\) : Air density
- \(S\) : Cross-sectional area of the object
- \(C_D\) : Drag coefficient at the current Mach number
- \(\mathbf{v}\) : Current elocity vector
- \(v\) : Magnitude of the velocity vector
- \(m\) : Mass of the object
- \(\mathbf{g}\) : Gravitational acceleration vector
Equation¶
\[
\frac{d\mathbf{v}}{dt} = \frac{- \frac{1}{2} \rho S C_D \mathbf{v}v}{m} - \mathbf{g}
\]
Description¶
The differential equation describes the change in velocity at each time step (\(\Delta t\)) of a point mass object experiencing only drag force and gravitational acceleration.