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I am building a 3D application that simulates launching small rockets. I want to draw their trajectories.

I know that rockets have a degree of stability. I want to include this in the simulation, but I don't know what the physics would look like.

How do I go about calculating a rocket's trajectory?

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is this actually a question for gamedev.SE? If you're looking for realistic physical models for rocket trajectories physics.SE might be of more help. Accurate physical simulations of air turbulence and vorticity are not easy. Unless you just need something that looks close enough to an unstable rocket trajectory. – Jimmy Jan 16 '13 at 22:14

I would take a physics engine, model rocket, add force to jet and just save state in a list of time points. Its no need to be in runtime, you can change parameters from code.

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I can think of three interesting paths to plot:

  1. the projected path of the rocket at launch,
  2. the projected path of the rocket from the current point in time,
  3. and the path traveled by the rocket so far.

From any point in time, you can project where the rocket will land by stepping forward and assuming constant flying conditions.

But as the rocket actually moves, you'll likely want to add in slight random fluctuations in things like wind strength and direction, and perhaps imperfect burn from the rocket itself, and this introduces error between the projected path and the actual path.

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