The article will research a lander flying into the atmosphere with flow velocity constraint, . the total load by means of minimizing the total thermal energy at the end of the landing process. The lander’s distance at the last moment depends on the variables selected from the total thermal energy minima. | Journal of Computer Science and Cybernetics, , (2015), 357 364 DOI: THE MINIMUM TOTAL HEATING LANDER DANG THI MAI Faculty of Basic Sciences - University of Transport and Communications; The article will research a lander flying into the atmosphere with flow velocity constraint, . the total load by means of minimizing the total thermal energy at the end of the landing process. The lander’s distance at the last moment depends on the variables selected from the total thermal energy minima. To deal with the problem, the Pontryagin maximum principle and scheme Dubovitskij Milutin will be applied. Boundary value problems are solved by the introduction and continuation of the perturbation parameters and solutions for the selected parameter. The results of simulations perform on Matlab. Keywords. Maximum principle, control, the overload, total heat, minimum. Abstract. 1. INTRODUCTION Research is on the problem of choosing an angle to launch the flying object which is reducing velocity in atmospheric conditions under which the minimizing of total heat flow with the load limits of aircraft equipment is taken into account. The total heat output of the device is the integral form of the following: T 1 (1) CV 3 ρ 2 dt Q= 0 Required to detemine a control Cy (t), which minimizes Q(T ) (1) under the following restrictions: nσ = 2 2˙ C(x) + Cy q S ≤ N, G min max Cy ≤ Cy ≤ Cy , ρ = ρ0 e−βH , g = g0 S ˙ θ = Cy q + mV q= ρV 2 , 2 G = mg, 2 Cx = Cx0 + kCy , R2 , (R + H)2 V g − R+H V (2) (3) S ˙ V − Cx q − g sin θ m (4) ˙ cos θ, H = V sin θ (5) RV cos θ ˙ L= (6) R+H where nσ - full overload, q - speed pressure, ρ - atmospheric density, V - velocity of the vehicle, θ path angle, H− height, L - the remote, G- the weight of the machine, m − − mass, g0 - acceleration due to gravity on the surface of the planet, R - the radius of the planet, Cx - the drag coefficient, Cy min max lift coefficient, S - .
