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I'm working on a small game as a hobby project, and I've run into a problem that would seem simple, to me, but that I can't find any information on or solution to.

Multiple force on one object

How would one go about figuring out what happens to this object, in terms of movement and rotation?

I have a lot of (bad) ideas, but I think I'll hold them back and just leave it at that. This is my first post here, sorry if it's inappropriate etc. (Please let me know.)

(PS. Yes, it's a space game with small ships with many engines : )

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I do not know if you remember Newton's second law from high school physics: $$ \sum{\vec{F}}=m\vec{a} $$ where $\vec{a}$ is the acceleration of the center of mass.
And similarly there is also a relation for angular acceleration: $$ \sum{\tau}=I\alpha $$ where $\tau$ is torque and $I$ is the moment of inertia around the center of mass.

This assumes that your game is 2D. However in 3D the torque becomes a vector, just as the angular acceleration and moment of inertia becomes a tensor.

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  • $\begingroup$ Thanks! Hm, so I know how to sum all forces as if they were all applied to the COM, and how to calculate torques and balance them out for a net torque. Is that all I need to do? (I have this hunch the total energy of the system must be what is put in, but it feels like I get rotational energy "for free" then?) $\endgroup$
    – 0scar
    Commented Jan 11, 2014 at 16:49
  • $\begingroup$ If the body is rotating then the forces applied of center will perform more work than if they where applied in line with the COM. This extra work is compensated by the amount of rotational energy. So the conservation of energy still holds. $\endgroup$
    – fibonatic
    Commented Jan 11, 2014 at 17:10
  • $\begingroup$ @fibonatic I think in your last sentence there's an imprecision: in $3D$ the correct equation would be $\sum \tau = \frac{d}{dt}(I\omega )$, that gives Euler's equations. $\endgroup$
    – pppqqq
    Commented Jan 11, 2014 at 19:07
  • $\begingroup$ Possibly useful: gafferongames.com/game-physics/physics-in-3d $\endgroup$
    – BMS
    Commented Jan 11, 2014 at 19:42

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