The Cubic Spline Functions in Classical Dynamical Studies

Pa is the mass associated with the coordinate Q. The first type hamiltonian equa- 

Suppose now, that the potential V is spline fitted We consider the general polydimensional case and that the number of mesh points in all directions are equivalent to infinity (N - oo). This situation is always attainable from a polydimensional grid of computed values in a sufficient quantity by subdivision of the step in each direction and preliminary interpolation of purely numerical supplementary values to be used in the spline expression, which therefore is  

The partial derivatives required by Eq. (26) then are very simply expressed for instance  

The local variable Ua = lies within the limits — 4 and + —. Values of B s and 

The algorithm is readily programmed. It allows for dynamical studies with non empirical potentials whatever the dimensionality of the problem under consideration. 

In the two-dimensional case, McLaughlin and Thompson recently used an elegant and convenient matrical method given by Jordan and de Boor  

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