Inverse Problems in Ordinary Differential Equations and Applications

This book is dedicated to study the inverse problem of ordinarydifferential equations, that is it focuses in finding all ordinary differentialequations that satisfy a given set of properties. The Nambu bracket is thecentral tool in developing this approach. The authors start characterizing theordinary differential equations in R^N which have a given set of partialintegrals or first integrals. The results obtained are applied first to planarpolynomial differential systems with a given set of such integrals, second tosolve the 16th Hilbert problem restricted to generic algebraic limit cycles,third for solving the inverse problem for constrained Lagrangian andHamiltonian mechanical systems, fourth for studying the integrability of aconstrained rigid body. Finally the authors conclude with an analysis onnonholonomic mechanics, a generalization of the Hamiltonian principle, and thestatement an solution of the inverse problem in vakonomic mechanics.