The Impetus-Striction Formulation of Constrained Dynamics: Unconstrained Hamiltonian Descriptions of Constrained Lagrangian Dynamics

Prof. J. H. Maddocks
Institut de Mathematiques Bernoulli
Swiss Federal of Institute of Technology
1015 Lausanne, Switzerland

In constrained Lagrangian dynamics there is some freedom in the choice of conjugate variable used to transform to an associated Hamiltonian formulation. I will show how to use this freedom to construct Hamiltonian descriptions of constrained Lagrangian dynamics in which the constraint is either transformed to an integral, or to an attractive invariant manifold of the dynamics. This impetus-striction formulation has already proven useful in analytical work concerned with various infinite-dimensional (i.e. PDE) systems arising in continuum mechanics, both involving equality and inequality constraints. Whether the impetus-striction approach could be of practical use in complicated finite-dimensional systems such as Molecular Dynamics is an open question.

References

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