Over the last few days, I've been trying to understand how applying forces to a system of point masses will effect the system's linear and angular velocity in 3 dimensions. I came across this answer that described a solution for a rigid bar in 2 dimensions. From this I believe I could figure out the velocities that I need, however with my relatively limited knowledge of physics, I'm having difficulties translating the solution into 3 dimensions. How could I go about doing so?
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So you mean, you are having your masses lying on a three dimensional space on one 3-d position vector $r$. Easy. Just break up the vector into its components using trigonometry, break up the masses, or rather, break up the effective inertia of the total mass, and then you solve for any variable you want. In case you're wondering how the heck angular momentum gets broken, remember it is just a perpendicular vector and it can be broken up into components perpendicular to the position vector's components easily.
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For linear acceleration you can always use Newton's second law, assuming relativistic effects can be neglected,
$$ \sum \vec{F}_\textrm{external} = m\,\vec{a}. \tag{1} $$
For the rotation you could use Euler's equation of rotation,
$$ \dot{\vec{\omega}} = I^{-1}\left(\sum M_\textrm{external} - \vec{\omega}\times(I\cdot\vec{\omega})\right), \tag{2} $$
with $I$ the moments of inertia tensor, $\vec{\omega}$ the angular velocity vector and each moment is calculated around the center of mass of the (rigid) body.
fibonatic
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