Shooting-projection method for a small object moving under the influence of a force
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2021-09-20
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Abstract
We consider a small object in 3D moving under the influence of a force that may depend explicitly on time, on the position of the object, and on its velocity. The equations of motion of classical mechanics are assumed to hold. If the position of the object is specified at some initial and some final time, obtaining the trajectory of the object requires the solution of a two-point boundary value problem. To solve the problem various numerical technics can be applied. This paper extends the recently proposed shooting-projection method to 3D. We introduce a Lagrangian from which, applying the principle of least action, the projection trajectory is derived. Analysis of the action reveals the meaning of the projection trajectory. Using the shooting-projection method, the considered two-point boundary value problem is solved for the case of a projectile motion in the presence of air resistance and wind.