Flight range maximization problem for a simplified aircraft model

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Resumo

The flight range maximization problem for a simplified aircraft model is considered, considering the influence of the amount of fuel on the dynamics of the center of mass. It is assumed that the motion occurs in a vertical plane under the influence of homogeneous gravity forces and homogeneous resistance of the medium. In addition, there are an active thrust force and the ability to change the angle of inclination of the trajectory. These parameters are accepted as controls. An area in the space of initial variables is constructed, for which the problem of optimal synthesis is solved. It is shown that in this area the thrust can be of maximum value, zero value or singular value. The number and consequence of the trajectory arcs with the corresponding thrust have been established.

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Sobre autores

E. Malykh

Lomonosov Moscow State University

Autor responsável pela correspondência
Email: wyvling@gmail.com
Rússia, Moscow

O. Cherkasov

Lomonosov Moscow State University; Shenzhen MSU-BIT University

Email: oyuche@yandex.ru
Rússia, Moscow; Shenzhen, China

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2. Fig. 1. Acting forces and variables

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3. Fig. 2. Special control surface

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4. Fig. 3. Phase portrait of the system (4.3)

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5. 4. Extreme trajectory in space (θ, v, m) for v(0) = 0.4, m(0) = 2, m(T) = 1, v = 2, T = 1.5

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6. 5. Extreme trajectory in the (x, y) plane for v(0) = 0.4, m(0) = 2, m(T) = 1, u = 2, T = 1.5

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7. 6. Change of thrust over time (u, t) on an extreme trajectory for v(0) = 0.4, m(0) = 2, m(T) = 1, u = 2, T = 1.5

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8. 7. Extreme trajectory in space (θ, v, m) for v(0) = 0.75, m(0) = 2, m(T) = 1.25, v = 2, T = 3

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9. 8. Extreme trajectory in the (x, y) plane for v(0) = 0.75, m(0) = 2, m(T) = 1.25, v = 2, T = 3

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10. 9. Change in thrust over time (u, t) on an extreme trajectory for v(0) = 0.75, m(0) = 2, m(T) = 1.25, u = 2, T = 3

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11. 10. Extreme trajectory in space (θ, v, m) for v(0) = 1, m(0) = 2, m(T) = 1.25, v = 2, T = 1.25

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12. 11. Extreme trajectory in the (x, y) plane for v(0) = 1, m(0) = 2, m(T) = 1.25, u = 2, T = 1.25

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13. Fig. 12. Thrust change over time (u, t) on an extreme trajectory for v(0) = 1, m(0) = 2, m(T) = 1.25, u = 2, T = 1.25

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14. 13. Extreme trajectory in space (θ, v, m) for v(0) = 0.2, m(0) = 2, m(T) = 1.5, v = 2, T = 4

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15. 14. Extreme trajectory in the (x, y) plane for v(0) = 0.2, m(0) = 2, m(T) = 1.5, v = 2, T = 4

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16. Fig. 15. Thrust change over time (u, t) on an extreme trajectory for v(0) = 0.2, m(0) = 2, m(T) = 1.5, u = 2, T = 4

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