In industry, a crucial phase in the design of a complex mechanical system, such as a multibody spacecraft, a robotic device, or a mechanism, is the formulation of exact, nonlinear, differential equations of motion of the system for use in attitude dynamics simulations and for linearization as a prelude to control system design. Because these systems are complex, the classical (e.g., Newtonian, Lagrangian, Hamiltonian, etc.) methods for formulating the associated equations of motion require so much labor and/or lead to such complicated equations that these methods are not usable in engineering practice. In contrast, Kane’s method for formulating equations of motion does not suffer from the shortcomings of the classical methods and, consequently, has become the industry standard. Moreover, Kane’s method, the foundation of which rests on the simplest of kinematical ideas, is much easier to teach and to learn than the classical approaches, and, hence, can be found in the mechanical and aerospace engineering curricula at many major universities. Despite this, many engineering, physics, and mathematics faculty members and their students are unfamiliar with Kane’s method, probably because the dynamics problems they encounter in academic work rarely reach the level of complexity that renders intractable the classical methods they routinely employ.
It is the purpose of this talk to bring to light the shortcomings of the classical methods when applied to the task of formulating equations of motion of complex systems, and to give a brief overview of Kane’s method.
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David A. Levinson holds the position of Senior Staff Research Engineer at the Lockheed Martin Missiles and Space Advanced Technology Center in Palo Alto, California, where he is responsible for producing special purpose computer programs for predicting motions of complex mechanical systems, such as multibody spacecraft, robotic devices, and aerospace mechanisms.
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Over the years, he has been the recipient of numerous engineering awards, among them the American Institute of Aeronautics and Astronautics (AIAA) San Francisco Section Outstanding Young Engineer Award, the AIAA San Francisco Section Engineer of the Year Award in Astronautics, the AIAA San Francisco Section Engineering Educator of the Year Award, the American Society of Mechanical Engineers (ASME) Santa Clara Valley Section Distinguished Mechanical Engineer Award, the American Astronautical Society Outstanding Achievement Award, and the Lockheed Missiles and Space Company President’s Award.
He is the author or coauthor of 43 published technical papers, a coauthor of the two McGraw-Hill textbooks, Spacecraft Dynamics and Dynamics: Theory and Applications, and a coauthor of the desktop-published textbooks, Dynamics Online: Theory and Implementation with AUTOLEV, Engineering Mechanics Online: Part 1, Engineering Mechanics Online: Part 2, and AUTOLEV User's Manual. Mr. Levinson is a Fellow of both the American Astronautical Society and the ASME, and is an Associate Fellow of the AIAA. He currently is chairman of the Discover "E" K-12 engineering outreach program for the Silicon Valley Engineering Council. Mr. Levinson is in demand nationally and internationally as a speaker, and was an ASME Distinguished Lecturer from 2000 through 2004. He is well known for his unusual ability to explain complex ideas to general audiences in an informative and entertaining way. For over thirty years he has lectured on technical subjects to a wide variety of audiences, including Cub Scouts, engineering graduate students, swimming coaches, physicians, high school students, teachers, university professors, Kiwanis Clubs, and fifth graders. |
