Abstract
In applied mathematics and mechanical engineering we normally think of numerical calculations if computers are involved. Although simulations by means of numerical methods are powerful tools for investigations in mechanics, they do have drawbacks, e.g. finite precision, errors generated when evaluating expressions. General global results or proofs of theoretical results cannot be obtained from simulations.
A broader understanding of mechanical phenomena can be gained by means of analytical methods. But even for seemingly simple mathematical models, analytical calculations by paper and pencil may become very time-consuming, may be the source of many errors, and will sometimes be impossible. In such cases, computerized symbolic manipulation is clearly faster as well as safer and therefore preferable. But often, purely symbolical investigations cannot fulfill all of our needs in mechanics. Therefore, a semi-analytical approach, combining the features of analytical and numerical computations, is a most desirable synthesis. This allows the analytic work to be pushed further before numerical computations start.
The aim of the course is to present important software tools, basic concepts, methods, and applications of computerized symbolic manipulation to mechanics problems. A survey on different approaches and possibilities for symbol manipulation is followed by a review of all major general purpose software packages. Lectures on generation of equations of motion, structural mechanics in general, analysis of nonlinear dynamic systems, and perturbation methods represent some of the most advanced applications of symbol manipulation methods. The main objective of this course is to encourage the use of symbolic manipulation in the analysis of mechanical systems.
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Kreuzer, E.J. (1994). Generation of Symbolic Equations of Motion of Multibody Systems. In: Kreuzer, E. (eds) Computerized Symbolic Manipulation in Mechanics. CISM International Centre for Mechanical Sciences, vol 343. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3010-0_1
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DOI: https://doi.org/10.1007/978-3-7091-3010-0_1
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