Variational principles for second-order differential equations : application of the Spencer theory to characterize variational sprays

In this book the author has tried to apply "a little imagination and thinking" to modelling dynamical phenomena from a classical atomic and molecular point of view. Nonlinearity is emphasized, as are phenomena which are elusive from the continuum mechanics point of view. FORTRAN programmes are provided in the appendices An introduction to formal integrability theory of partial differential systems; Frolicher-Nijenhuis theory of derivations; differential algebraic formalism of connections; necessary conditions for variational sprays; obstructions to the integrability of the Euler-Lagrange system; the classification of locally variational sprays on two-dimensional manifolds; Euler-Lagrange systems in the isotropic case