Bi-Hamiltonian Structure in Serret-Frenet Frame

Physics – Mathematical Physics

Scientific paper

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Scientific paper

We reduced the problem of constructing bi-Hamiltonian structure in three
dimensions to the solution of a Riccati equation in moving coordinates of
Serret-Frenet frame. We then show that either the linearly independent
solutions of the corresponding second order equation or the normal vectors of
the moving frame imply two compatible Poisson structures.

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