By Roger Brockett (auth.), Mark Alber, Bei Hu, Joachim Rosenthal (eds.)
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Extra resources for Current and Future Directions in Applied Mathematics
This study has led to major programs in the analysis of the spread of infectious disease in both human and animal populations. The strength of the program is that we have always had very strong assistance and encouragement from TTUHSC and from the both the city and state departments of public health. What can be gained from the experience at TTU? The first observation is that good applied mathematics can seldom be done alone-it is almost always a group effort. It is seldom that one person has the necessary background in sufficient areas to successfully attack a truly applied problem.
This calculation is straightforward using the definition. 5) where J is the uncontrolled momentum map (the momentum map for L) and jT,U is a correction term depending on T and a. In many examples a formula for jT,U can be computed directly and simply as we shall see, but we give the general formula for completeness. To explain it, first choose a basis ea , a = 1, ... , dimg for the Lie algebra g and write elements ~ E gas ~ = ~aea (summation understood) and choose coordinates qi, i = 1, ... , n on Q.
There are several active research themes of direct interest to the CDS faculty. One is the basic theory of dynamical systems, including bifurcations, stability, resonance and chaotic dynamics. This is applied to a number of problems including, for example, molecular systems and jet engine dynamics. Another theme is the use of geometric methods in the description and control of mechanical systems, including questions of stabilization, nonholonomic mechanical systems (mechanical systems with rolling constraints for instance) and the use of geometric phases to describe and design motion control systems.