## A New Method for Treating Optimal Trajectories with Restricted Segments, Issue 744 |

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### Contents

AN EXTENSION OF THE PROBLEM OF BOLZA | 3 |

Figure Page | 9 |

APPLICATIONS | 15 |

1 other sections not shown

### Common terms and phrases

aircraft Aircraft Flight Mechanics brachistochrone problem Calculus of Variations coasting arc coasting periods combined with equation constraint equations corner conditions corner points cot y2 discontinuous dynamical equations eliminated endpoint conditions equations of constraint equations of motion Euler equations applicable evaluated at point final flat earth following results Following the methods functional form defined given by equation Hamiltonian function inequality constraint initial values integrating the Euler jump Lagrange multipliers methods of Section MULTISTAGE ROCKET necessary optimizing conditions non-dimensional obtained optimal control law optimal solution optimal trajectory Point 2 dt points q previous section problem of Bolza restricted and unrestricted restricted arc restricted segments resulting trajectory satisfied second order constraint shown in Figure single control variable solved two-body problem unrestricted portion unrestricted trajectory usable information Variable Euler Equation Variations written as follows X.dy Xu2_ Xv2+ Xv3+ yield no usable yields the following zero