Hamiltonian mechanics

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  • As quantum theory enters its second century, it is fitting to examine just how far it has come as a tool for the chemist. Beginning with Max Planck’s agonizing conclusion in 1900 that linked energy emission in discreet bundles to the resultant black-body radiation curve, a body of knowledge has developed with profound consequences in our ability to understand nature. In the early years, quantum theory was the providence of physicists and certain breeds of physical chemists. While physicists honed and refined the theory and studied...

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  • Financial markets have undergone tremendous growth and dramatic changes in the past two decades, with the volume of daily trading in currency markets hitting over a trillion US dollars and hundreds of billions of dollars in bond and stock markets. Deregulation and globalization have led to large-scale capital flows; this has raised new problems for finance as well as has further spurred competition among banks and financial institutions.

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  • One of the important tools of geometric mechanics is reduction theory (either Lagrangian or Hamiltonian),which provides a well-developed method for dealing with dynamic constraints. In this theory the dynamic constraints and the sym- metry group are used to lower the dimension of the system by constructing an associated reduced system. We develop the Lagrangian version of this theory for nonholonomic systems in this paper. We have focussed on Lagrangian systems because this is a convenient context for applications to control theory. ...

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