November 1996  ICTCM IX (Reno)  9

Mathematical Formulation

• 2nd-order ODE

mx′′ = −mg − kx′
x(0) = x_{0}
x′(0) = 0

• 1st-order system

\begin{aligned}x′ & = & v, & x(0) = x_{0} \\ v′ & = & −g − \frac{k}{m}v, & v(0) = 0 \end{aligned}

• k — piecewise constant coefficient of air resistance

k(t) = \{ \begin{matrix}k_{1}, & t < t_{d} \\ k_{2}, & t ≥ t_{d} \end{matrix}

• t_{d} — time of (instantaneous) deployment