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Extended System Motion

We have developed the following two equations of motion which can provide a basis for analyzing general motion of an extended system:

1. The net external force on the system produces a translation of the center-of-mass of the system in an inertial frame, given by,

F = M a_CM

2. The torque due to external forces about a fixed origin O (in space) produces a rotational motion in the system, which is described by

The above two vector equations are equivalent to six scalar equations (in component form). Hence, these are not sufficient to determine the variation of all the 3n co-ordinates of n-particle non-rigid system. The equations are sufficient to analyze the motion of a system which can be described by a maximum of six independent of c-ordinates. Such an extended system is a rigid body.