Scholarpedia · 2015 · 559 citations · 0 references
Natural SciencesMathematicsPhysicsDynamical SystemsMathematical PhysicsTheoretical PhysicsHamiltonian MechanicsHamiltonian SystemsLagrangian DynamicsLagrangian MechanicsVariational FormulationVariational PrinciplesCanonical Variational FormulationConstraints In Hamiltonian SystemsContinuum Field ModelsField LagrangiansField Theoretic Hamiltonian SystemsHamiltonian Partial Differential EquationsHigher-order LagrangiansLagrangian Systems
Ostrogradsky's construction of a Hamiltonian formalism for nondegenerate higher derivative Lagrangians is reviewed. The resulting instability imposes by far the most powerful restriction on fundamental, interacting, continuum Lagrangian field theories. A discussion is given of the problems raised by attempts to evade this restriction.