Jacobi fields for second-order differential equations on Lie algebroids (Q260751)

In the classical Riemannian geometry Jacobi fields along geodesics play a very important role. From the point of view of differential equations a geodesic is a second order differential equation, so is the Jacobi equation of which Jacobi fields are solutions.NEWLINENEWLINEThe authors present a generalization of these results and ideas to the framework of general second order differential equations on manifolds. They try to diverge as little as possible from the main ideas behind the classical Jacobi equation, in particular they formulate the corresponding variational principle.NEWLINENEWLINEThe obtained results the authors apply in the framework of Lie algebroids and arrive at an equation which is valid for second order systems with holonomic constraints.