Inverse Problems in Ordinary Differential Equations and Applications

This book focuses on finding all ordinary differential equations that satisfy a given set of properties, thus dedicating itself to inverse problems of ordinary differential equations. The Nambu bracket acts as the central tool to the authors’ approach. The book begins with a characterization of ordinary differential equations in R^N which have a given set of M=N partial and first integrals, before addressing planar polynomial differential systems with a given set of polynomial partial integrals. The authors then go on to solve the 16th Hilbert problem (restricted to algebraic limit cycles) based on generic assumptions, followed by a study of the inverse problem for constrained Lagrange mechanics and Hamiltonian systems, as well as the issue of the integrability of a constrained rigid body. The book concludes with an analysis of transpositional relations, a generalization of the Hamiltonian principle, as well as the inverse problem in vakonomic mechanics.