Design of Trajectory Optimization Approach for Space Maneuver Vehicle Skip Entry Problems by Runqi Chai & Al Savvaris & Antonios Tsourdos & Senchun Chai

Author:Runqi Chai & Al Savvaris & Antonios Tsourdos & Senchun Chai
Language: eng
Format: epub
ISBN: 9789811398452
Publisher: Springer Singapore

Proof

Since the final time is a free variable, there is a stationary condition for the function. This condition is obtained by applying the endpoint Lagrangian equation (e.g., ). For the problem studied in this project, this equation can be rewritten as

(5.21)

Equation (5.21) implies that the final value of the Hamiltonian function should be −1 for this problem. Then the Hamiltonian evolution equation is used to demonstrate the behavior of the Hamiltonian with respect to time such that

(5.22)

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