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What is the best coordinate system for describing the projectile motion? Rectangular coordinate system or n-t(normal and tangential) coordinate system.

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  • $\begingroup$ Personally i find the latter better. $\endgroup$
    – user74370
    Commented May 24, 2015 at 5:13
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    $\begingroup$ This seems primarily opinion-based as both descriptions are equivalent. $\endgroup$
    – ACuriousMind
    Commented May 24, 2015 at 12:51

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For a particle in a gravitational field treated as a constant? Surely Newton's equations of motion in the fixed rectangular frame:

$$\ddot{x}=0$$ $$\ddot{y}=-g$$

are as simple as it can get!

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  • $\begingroup$ By constant particle do you mean that tnis system is not best for missiles's motion lets say an example. $\endgroup$ Commented May 24, 2015 at 7:40
  • $\begingroup$ @SohailAhmed I mean that the gravitational field is treated as a constant $g$, as opposed to a gravitational field which might go like $\frac{\hat{r}}{r^2}$. The second case is a lot more complicated. $\endgroup$
    – user12029
    Commented May 24, 2015 at 16:13
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If the range is not too large, you can approximate the acceleration (due to gravity) vector to have the same direction over the trajectory of the projectile. It will probably be a good idea to use earth fixed 2D cartesian coordinates in this case, one axis horizontal and the other vertical to the Earth's surface. The acceleration acts only along the vertical direction. The motion projected onto the horizontal direction becomes free of acceleration.

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