A total understanding of rotating machinery vibration analysis requires evaluation of critical speed placement, forced response sensitivity to imbalance, linear onset of instability prediction and full non-linear response analysis. Of these four areas of analysis, only the first three are applied as a basic design tool in modern turbo-machinery analysis. The prediction of multi-mass flexible rotor steady-state elliptic orbit response, including bearing damping and support flexibility, has been and remains in this author’s opinion, to be the basic workhorse and keystone of machinery design. This has now been true for over 35 years. The person responsible for developing this basic method of analysis has been a longtime friend of many engineers worldwide. This paper is written to acknowledge this contribution, one of many in fact, made by Jorgen W. Lund and is presented in memory of his life’s work at this occasion of honoring his contributions to our profession. The utility of the analysis will be discussed and the powerful insight it gives to complex machinery dynamic behavior will be illustrated.