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The phrase "trajectory with" is correct and usable in written English.
You can use it to refer to the path that an object or person follows. For example, "The rocket launched, following a trajectory with a high apogee."
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We're on a similar trajectory with our debt.
South Carolinians are hoping for a similar trajectory with Boeing.
Below, Mac discusses his career trajectory with Charlie Rose in a 2002 interview.
The video, using images from Google Maps, outlines the suspect's trajectory with a red dot.
A limit cycle is a closed trajectory with a couple of extra hypotheses.
Condos haven't followed the same trajectory, with many developers building larger units to attract buyers.
Her evolution as a more pop-oriented artist continues its trajectory with her new release, "Dreaming of Revenge".
Yet "Invincible" counters its predictably inspirational trajectory with close attention to historical detail and blue-collar hardship.
In an emergency, the crew, led by Malenchenko, had the ability to alter their trajectory with a hand controller.
Moreover, the moving mass may travel at any arbitrary trajectory with no restriction.
Then, we combine the upward trajectory with a stabilizing trajectory to make a complete trajectory.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com