A new geometrical look at Ostrogradsky procedure

TL;DR

This paper revisits Ostrogradsky's Hamiltonian formulation for higher-order Lagrangians using modern non-holonomic geometry and constrained variational calculus, providing a new geometric perspective.

Contribution

It introduces a geometric reinterpretation of Ostrogradsky's procedure leveraging advanced differential geometric methods.

Findings

Provides a new geometric framework for Ostrogradsky's formulation

Clarifies the structure of higher-order Lagrangian systems

Enhances understanding of constrained variational calculus in this context

Abstract

Making use of the modern techniques of non-holonomic geometry and constrained variational calculus, a revisitation of Ostrogradsky's Hamiltonian formulation of the evolution equations determined by a Lagrangian of order >= 2 in the derivatives of the configuration variables is presented.