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Consider a simple point mass of $M$ in vacuum in 1-dimension with initial position $x_0$, velocity $v_0$ and acceleration $a_0$. Our goal is to move this body to position $x_1$ with velocity $v_1$ and acceleration $a_1$ in minimum possible time. To do this, we are allowed to apply any force we desire on this body, $F(t)$ with two constraints $|F(t)| < P$ and $|F^\prime(t)| < Q$. How do we find $F(t)$ in this specific problem?

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  • $\begingroup$ You are correct, it seems I oversimplified the problem. In the actual real life scenario I have constraint on maximum available force as well as maximum possible rate of change in force. I think the second condition would also possibly make sure F(t) is continuous. I have added these constraints in the question now. $\endgroup$ Jun 29, 2018 at 11:48

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