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Introduction The first is the increased need to model and analyze complex, multibodied and often elastic-bodied structures, such as satellites, robot manipulators, and vehicles. The second is the proliferation of the digital computer, hich has led to the development of numerical techniques to derive the describing quations of a system, integrate the equations of motion, and obtain the response This new computational capability has encouraged scientists and engineers to model and numerically analyze complex dynamical systems which in the past either could not be analyzed, or were analyzed using gross simplifications The prospect of using computational techniques to model a dynamical system has also led dynamicists to reconsider existing methods of obtaining equations of motion.

When evaluated in terms of systematic application, ease of implementation by computers, and computational effort, some of the traditional approaches lose part of their appeal. This approach is computationally inefficient.

Moreover certain terms in the differentiation of the kinetic energy cancel each other, resulting in wasted manipulations As a result of the reevaluation of the methods used in dynamics, new approaches have been proposed and certain older approaches that were not commonly used in the past have been brought back into the limelight. What has followed in the literature is a series of papers and books containing claims by proponents of certain methods, each extolling the virtues of one approach over the other without a fair and balanced nalysis.

This, at least in the opinion of this author, has not led to a healthy envi ronment and fruitful exchange of ideas. It is now possible for basic graduate level courses in dynamics to be taught at different schools with entirely different subject material These developments of recent years have inspired me to compile my lecture notes into a textbook.

Realizing that much of the research done lately in the field of dynamics has been reported very subjectively, i have tried to present in this book a fair and balanced description of dynamics problems and formulations, from the classical methods to thc newer techniqucs used in todays multibody environments I have emphasized the need to know both the classical methods as well as the newer techniques and have shown that these approaches are really complementary.

Having the knowledge and experience to look at a problem in a number of ways not onl facilitates the solution but also provides a better perspective. For example, the book discusses euler parameters, which lead to fewer singularities in the solution and which lend themselves to more efficient computer implementation xii.


Analytical dynamics



First Chapter


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