# Goddart's rocket problem (TACO)

From mintOC

This page contains a model of the Goddart's rocket problem in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions. The original model using a collocation formulation can be found in the COPS library. Note that you will need to include a generic AMPL/TACO support file, OptimalControl.mod. To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

### AMPL

This is the source file goddart_taco.mod

# ---------------------------------------------------------------- # Rocket problem of Goddart using AMPL and TACO # (c) Christian Kirches, Sven Leyffer # # Source: COPS 3.1 collocation formulation - March 2004 # ---------------------------------------------------------------- include OptimalControl.mod; var t; var tf := 1.0, >= 0.01, <= 1; param v0 := 0.0; param m0 := 1.0; param g0 := 1.0; param h0 := 1.0; param hc := 500.0; param vc := 620.0; param mc := 0.6; param Tmax := 3.5*g0*m0; param c := 0.5*sqrt(g0*h0); param mf := mc*m0; var h >= h0, := 1; let h.interp_to := h0; var v >= v0; let v.interp_to := v0; var m <= m0; let m.interp_to := mf; var T >= 0, <= Tmax, := Tmax/2; let T.type := "u0"; param Dc := 0.5*vc*m0/g0; var D = Dc*v^2*exp(-hc*(h-h0)/h0); var g = g0*(h0/h)^2; maximize FinalHeight: eval(h,tf); let FinalHeight.scale := 0.01; subject to dh: diff(h,t) = v; dv: diff(v,t) = (T - D)/m - g; dm: diff(m,t) = -T/c; ih: eval(h,0) = h0; iv: eval(v,0) = v0; im: eval(m,0) = m0; fm: eval(m,tf) = mf; option solver ...; solve;

## Other Descriptions

Other descriptions of this problem are available in

- Mathematical notation at Goddart's rocket problem
- AMPL (using a fixed discretization) at the COPS library