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How can I get a function of time for coordinates of a 2D-moving body in a gravitational field from equations of forces?

I am having a hard time with writing code for simulation of 2D motion of a body with mass in a gravitational field of another body. I have 2 masses and a gravitational force equation. I know that ...
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Need help with a complex 3d scene (using Ogre and bullet)

In my setup there is a box with a hole on one side, and a freely movable "stick" (or bar, tube). This stick can be inserted/moved through the hole into the box. This hole is exactly as wide as the ...
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Run a few seconds of simulation just after loading a scene

I'm looking for a way to execute 3 to 15 seconds of simulation once a scene is loaded. The problem is: some objects can be left suspended in motion while the player exits the scene. their state is ...