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The regularization of the second order Lagrangians in example. (English) Zbl 1369.49070
This paper deals with a geometric formulation of the regular third order Hamiltonian systems for a given second order Lagrangian. A regularization method is illustrated on concrete examples of the Lagrangian which is quadratic in second derivatives. The arguments combine Dedecker-Hamilton extremals, Lepagean equivalents and Poincaré-Cartan forms.
MSC:
49S05 Variational principles of physics
35R01 PDEs on manifolds
53Z05 Applications of differential geometry to physics
70H30 Other variational principles in mechanics
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