Optimization Problem of a Sea vehicle Entry into Water

For a vehicle diving into the sea, the variation of velocity with horizontal distance covered was studied, the conditions being that the vehicle requires minimum time and that the horizontal distance is fixed. The variation of the vehicle's trajectory angle and time versus depth was also investigated. The variational problem makes use of the isoperimetric condition. The second-order differential equation was solved by the Runge-Kutta-Nystrom. method and the isoperimetric condition by Simpson's rule