M. Crâ \c sm\u areanu

Adjoint variables: a common way to first integrals and inverse problems

We obtain a type of first integrals for ODE by using a generalization of the method of adjoint variables to higher-order systems. A generalization of the harmonic oscillator and a classical spinning particle is completely discussed in order to solve the associated inverse problem.

Mathematics Subject Classification: 34A34, 34A30, 70D99.

Key words and phrases: First integral, adjoint system, system in kinematical form, inverse problem, harmonic oscilator, spinning particle.