# Movement of connected masses under external force

Hello,

First time post here, so if I violate some rules of protocol etc. please forgive and let me know! Anyway, I've been asking profs and other physicists this question, and the more-knowledgable the person I ask, the more complex the answer sounds!

Two basic setups:
(1) two masses, connected by a massless rod, resting on a plane, no friction, etc. etc. apply a force off the center-of-mass. I know it will translate and rotate...but what are the equations for describing the rotation? (translation is just F=ma, right?); and
(2) say you have three masses M1 M2 M3; M1 and M2 joined by a rod; M2 and M3 joined by a rod; but the rods can pivot (in a plane) where they're attached to the masses. Think atoms maybe: M1-r1-M2-r2-M3 and M1, M2 and M3 can move around, so the angle between the rods can be whatever. Start off with M1 M2 M3 all alligned. Now I apply a force to M3, perp. to the line of masses. What is the motion?

My question is general: I'm heading towards a 2-D or 3-D lattice of such masses and rods, where some pivots are free, some have resistance, some are fixed; and I want to apply a force somewhere and model the motion. I don't expect a closed form solution! I just want to know if there's a reasonably-simple way to model this, say, across a small time interval, maybe study the effect at the application point and the immediately-connected masses, then propagate that to the adjacent masses, and so on.

Sorry if this is a ridiculous question (either too simple or too complex). I'm pretty stuck, but really need to model this. Any help would be greatly appreciated! Thanks...

vanesch
Staff Emeritus