Analysis of Curve Trajectory - Is It Correct?

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The analysis presented in the image is questioned for its accuracy regarding curve trajectory. It is clarified that if a second force is applied at the center of mass, it will result in downward acceleration without causing torque. However, if the force is applied forward of the center of mass, it will induce both downward acceleration and torque, leading to rotation of the ship. The discussion emphasizes that the placement of the thruster determines the outcome, with two distinct scenarios based on its position. Understanding these dynamics is crucial for accurate analysis of reaction control systems.
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I want to know whether this analysis in the image is correct or no ,and if no pleas I want u to explain me the reason thank you ..
 

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this is a better picture that explains what I am really asking about ...
 

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#2 as long as the second force is applied at the center of mass. If it's applied foreward of the center of mass, it will not only cause the townward acceleration, but also the torque that would rotate the ship.

Basically, as you drew it, #2 is the solution. If you move the thruster foreward on the ship, #1 is the solution.
 
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