The geometry of higher-order Lagrange spaces: applications to mechanics and physics

This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1 A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with Applications to higher-order analytical mechanics and theoretical physics are included as well Audience This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology