Abstract
The inverse problem for the airplane planner motion is analyzed through direct application of Hamilton's law of varying action. Using this technique one can approach the problem by solving a set of nonlinear algebraic equations only; i.e. no differential equations are needed. In this case the mass center trajectory and the required controls are approximated as a truncated power series. Direct application of Hamilton's law establishes the governing relations between those input and output coefficients. The problem is then solved in the coefficient domain to obtain the unknown control coefficients. The problem is formulated and solved for both time dependent and space dependent specified trajectories. Two illustrative numerical examples are provided to demonstrate the technique.
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