By Peter C. Hughes
From its roots in classical mechanics and reliance on balance thought to the evolution of functional stabilization principles, this quantity covers environmental torques encountered in house; strength dissipation; movement equations for 4 archetypical platforms; orientation parameters; illustrations of key thoughts with on-orbit flight facts; and common engineering undefined.
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2 MOTION EQUATIONS FOR A SYSTEM OF POINT MASSES, X9,, 49 We may abserve that aT _ a? (34) -bo using (32). This result is complementary to (27). Scalar Motion Equatlons Thus far in this section, we have avoided the expressions of our vector relations in terms of their components in specific reference frames. Experience shows that such compments are best not taken so long as manipulations are possible in vector terms. This strategy-defemng the choice of reference frame in which to express a given vector-is simply a matter of keeping one’s options open as long as possible.
At the same time, detailed solution for the system motion generally cannot proceed without reducing the motion equations to scalar form. These scalar equations are most conveniently expressed in matrix notation, whose compactness promotes a direct understanding of their structure. We have at present two reference frames at our disposal, q. Each vector and dyadic can be expressed in either frame; furthermore, the vector equations in which these vectors and dyadics appear can also be expressed in either frame.
N ) = (6) m=l Here, f n is no longer the total force on Pn;it is the force due only to agencies external to the system. A glance at Fig. , N ) m=l We sum these N equations to obtain p =f. + where N -f Cfn n=l is the total external force on the system. 1 for one particle. It should be observed that there is always a point, which we denote by @, about which the first moment of inertia vanishes. 2 MOTION EQUATIONS FOR A SYSTEM OF POINT MASSES,X9” 45 and Oiare given (Fig. 2) by For, by definition, N C mil& -~ c = ) 5 - m ~= c O, n=l as asserted.