I'm currently trying to solve the following two-point boundary problem by means of the shooting method:(adsbygoogle = window.adsbygoogle || []).push({});

To clarify, I'm investigating the optimal route of aerial/marine vehicles from one point to another point, considering a flow field.

* The starting and ending locations are set as x_{0}, y_{0}and x_{f}, y_{f}respectively.

* v is the constant speed of the vehicle relative to the field.

* A vector v=[v_{cx},v_{cy}]^{T}is used to describe the drift velocity of the field with respect to some coordinate system fixed to the ground.

* ψ is the vehicles navigation angle.

* The optimal change rate of the navigation angle has been found and is as follows:

There are two unknowns in this two-point boundary value problem, which are the initial navigation angle ψ(0) and t_{f}, which is the final time.

The problem that I would like some help with is thus the two-point boundary value problem that I want to solve by means of the shooting method. I haven't found useful and applicable sources that show me how to use the shooting method for this problem. I would very much appreciate a help in the right direction, either by some explanation or my directing me to useful sources.

Kind regards,

Ramos Pinto

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# I Two point boundary problem - Shooting method

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