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May 26th, 2017, 03:31 PM   #1
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Two point boundary problem - Shooting method

I'm currently trying to solve the following two-point boundary problem by means of the shooting method:



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 x0, y0 and xf, yf 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 vehicle's 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 tf, 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

Last edited by skipjack; May 27th, 2017 at 01:09 AM.
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May 27th, 2017, 08:52 AM   #2
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Any help will be greatly appreciated. Thanks in advance!
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