385 • 7 known axial -moment harmonic ratios applicable to 1 principal local DOF on each RWA   • 8 (at least) known radial -moment harmonic ratios applicable to 2 principal local DOF per RWA   • 20 viable flight -unit sets of IV datasets; a mix of partial ( i.e., due to penalty re- tests) and full   • 30 axial -DOF i solation system stiffness -damping combinations to evaluate; with and without isolators   • 34 radial -DOF isolation system stiffness -damping combinations to evaluate; with and without isolators  

Changing any single one of t hese elements/parameters results in a different jitter pass -fail value  compared  to specified limits. Based on prior results, none of  these individual  aspects could be readily  dismiss ed as  insignificant  in ferret ing out a previously undiscovered but potentially crucial LOS impact ing combination.   For one  specific example, most  results  (but not all) showed jitter-budget  peaks /threats  (withi n operational  frequencies) dominated by axial forces, where fine- balancing has no mitigating effect; a counterintuitive  outcome compared to conventional wisdom  that radial force unbalance is most likely  to threaten jitter. The  potential  permutations  seemed endless, most formidable being so many  harmonics present in the 5 RWA   DOFs. One fortunate aspect was, due to such low damping ( i.e., 0.005), the computed damped f requency  of a potential  high- jitter-response mode is  essentially equal  to its computed undamped frequency  (within  ~2-3%), therefore, jitter anal yses were constructed to evaluate response at each specific  computed mode  frequency (i.e., eigenvalues; 157 for full HST orbital model ), with inserts of  intermediate- increment values   smoothly  bridging the region between a computed mode peak and the  overtaking rising portion of the  nexthigher -frequency jitter spike (again, due to low damping’s very sharp  peak ). Once these means were  accomplish ed (in conjunction with a separate jitter assessment determining solid baselines  for 4 most -likely  flight RWAs with adequate data cho osing a representative and full  dataset  for each) , studies  shifted to  compare jitter results using  a robust subset containing the 4 most prominent  IV harmonic ratios ( i.e., 1.0,  2.0, 2.8, and 5.6 in 2 radial and 1 axial DOFs ) versus  an entire set  of detected harmonic ratios  (30 axial;  34  radial) . By comparatively using all harmonic ratios from a representative high- amplitude dataset for each  RWA DOF , results showed conclusively that 4 key harmonic ratios  (e.g., Fig. 9)  are excellent indicators for  RWA jitter predictions  and establishing a jitter baseline for  further  isolation and placement optimization  studies ; while maintaining timely and efficient computational processing and reporting14. 

Figure 9.  LOS Jitter Results using All RWA IV Harmonic Ratios  versus  Subset of 4 Key Ratios14  [Circles  are limited spots where 4 k ey ratios  under -predict  jitter spikes  compared to full-set results ]     Lessons Learned:  New ly-Refined  Correlative Analytical Investigation for RWA IV Key Harmonic s   Fundamental conjecture, based on first princ iples, initially supposed that residual unbalance coupled with  stringent bearing/retainer  tolerances define the means to successfully ensure low -IV rotating assemblies.  As this IV investigation demonstrated via statistically robust harmonic  ratio data mining, there is  much more  to this basic characterization for  a specialized  fine-pointing application. Knowing what IV output frequenci es,