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Studies of the dynamics of symmetric systems that can both deform in shape and rotate in space have driven much of the development of theoretical mechanics since the time of Newton. Examples range from the N-body problems of celestial and atomic and molecular physics through the rotating fluid systems from astrophysics and geophysics. In the last two decades key concepts that emerged from the 18th and 19th century, such as the existence of conserved quantities and the technique of phase space reduction, have been reinterpreted and generalized in an increasingly sophisticated geometric and analytic framework that can be applied to a wide range of practical problems. These ideas have also led to equally significant improvements in numerical techniques for studying mechanical system, the emphasis being on the development of robust methods for long time simulations which make full use of the underlying geometric structures.

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