Figure 1
δ method main algorithm.
Figure 2
Lunar lander on-off optimal control, Fourier, Chebyshev, Legendre results.
Figure 3
Lunar lander velocity, Fourier, Chebyshev, Legendre results.
Figure 4
Lunar lander height, Fourier, Chebyshev, Legendre results.
Figure 5
Lunar lander mass reduction, Fourier, Chebyshev, Legendre results.
Figure 6
Lunar lander on-of optimal control and switch function.
Figure 7
Reduction of Hamiltonian criterion δH for Fourier, Chebyshev, Legendre w.r.t iterations.
Figure 8
Reduction of δsH for Fourier, Chebyshev, Legendre w.r.t iterations.
Figure 9
Reduction of δsI for Fourier, Chebyshev, Legendre w.r.t iterations.
Figure 10
Reduction of the total cost function, for Fourier, Chebyshev, Legendre w.r.t iterations.
Figure 11
Lunar lander on-off optimal control, GA-PSO and ICA results.
Figure 12
Lunar lander velocity, GA-PSO and ICA results.
Figure 13
Lunar lander height, GA-PSO and ICA results.
Figure 14
Lunar lander mass reduction, GA-PSO and ICA results.
Figure 15
Reduction of the Hamiltonian, GA-PSO and ICA results.
Figure 16
Reduction of δsH,GA-PSO and ICA results.
Figure 17
Reduction of δsI, GA-PSO and ICA results.
Figure 18
Reduction of total cost function, GA-PSO and ICA results.
Figure 19
Schematic asteroid transfer in the Solar-centric polar coordinate.
Figure 20
Non-dimensiona lized radial distance.
Figure 21
Angular parameters in the polar coordinate.
Figure 22
Non-dimensiona lized radial velocity.
Figure 23
Non-dimensiona lized tangential velocity.
Figure 24
Non-dimensiona lized mass reduction.
Figure 25
Switch function and bang-bang thrust.
Figure 26
Non-dimension alized bang-bang thrust.
Figure 27
Thrust vector angle.
Figure 28
Reduction of δsI.
Figure 29
Reduction of the Hamiltonian w.r.t β, δu.
Figure 30
Reduction of δsH.
Figure 31
Reduction of the total cost function.
Figure 32
Time history of P(t) minimum-time and minimum-fuel.
Figure 33
Time history of ex(t), minimum-time and minimum-fuel.
Figure 34
Time history of ey(t), minimum-time and minimum-fuel.
Figure 35
Time history of hx(t), minimum-time and minimum-fuel.
Figure 36
Time history of hy(t), minimum-time and minimum-fuel.
Figure 37
Time history of semi major, minimum-time and minimum-fuel.
Figure 38
Time history of inclination, minimum-time and minimum-fuel.
Figure 39
Time history of eccentricity, minimum-time and minimum-fuel.
Figure 40
Time history of longitude of the ascending node, minimum-time and minimum-fuel.
Figure 41
Time history of argument of periapsis, minimum-time and minimum-fuel.
Figure 42
Reduction of ∂H/∂ψ or ∂1 to zero, minimum-time and minimum-fuel.
Figure 43
Reduction of ∂H/∂ψ or δ2 to zero, minimum-time and minimum-fuel.
Figure 44
Reduction of δsI to zero, minimum-fuel.
Figure 45
Reduction of δsH to zero, minimum-fuel.
Figure 46
Reduction of the main criteria, minimum-time and minimum-fuel.
Figure 47
Time history of optimal control angle ψ(t) (rad).
Figure 48
Time history of optimal control angle ψ(t) (rad).
Figure 49
Time history of optimal bang-bang control, normal thrust.
Figure 50
Time history of optimal bang-bang control, tangential thrust.
Figure 19
Schematic asteroid transfer in the Solar-centric polar coordinate.
Figure 20
Non-dimensiona lized radial distance.
Figure 21
Angular parameters in the polar coordinate.
Figure 22
Non-dimensiona lized radial velocity.
Figure 23
Non-dimensiona lized tangential velocity.
Figure 24
Non-dimensiona lized mass reduction.
Figure 25
Switch function and bang-bang thrust.
Figure 26
Non-dimension alized bang-bang thrust.
Figure 27
Thrust vector angle.
Figure 28
Reduction of δsI.
Figure 29
Reduction of the Hamiltonian w.r.t β, δu.
Figure 30
Reduction of δsH.
Figure 31
Reduction of the total cost function.
Figure 32
Time history of P(t) minimum-time and minimum-fuel.
Figure 33
Time history of ex(t), minimum-time and minimum-fuel.
Figure 34
Time history of ey(t), minimum-time and minimum-fuel.
Figure 35
Time history of hx(t), minimum-time and minimum-fuel.
Figure 36
Time history of hy(t), minimum-time and minimum-fuel.
Figure 37
Time history of semi major, minimum-time and minimum-fuel.
Figure 38
Time history of inclination, minimum-time and minimum-fuel.
Figure 39
Time history of eccentricity, minimum-time and minimum-fuel.
Figure 40
Time history of longitude of the ascending node, minimum-time and minimum-fuel.
Figure 41
Time history of argument of periapsis, minimum-time and minimum-fuel.
Figure 42
Reduction of ∂H/∂ψ or ∂1 to zero, minimum-time and minimum-fuel.
Figure 43
Reduction of ∂H/∂ψ or δ2 to zero, minimum-time and minimum-fuel.
Figure 44
Reduction of δsI to zero, minimum-fuel.
Figure 45
Reduction of δsH to zero, minimum-fuel.
Figure 46
Reduction of the main criteria, minimum-time and minimum-fuel.
Figure 47
Time history of optimal control angle ψ(t) (rad).
Figure 48
Time history of optimal control angle ψ(t) (rad).
Figure 49
Time history of optimal bang-bang control, normal thrust.
Figure 50
Time history of optimal bang-bang control, tangential thrust.