Related papers: Hamiltonian formulation of a class of constrained …

In the generalized Hamiltonian formalism by Dirac, the method of constructing the generator of local-symmetry transformations for systems with first- and second-class constraints (without restrictions on the algebra of constraints) is…

We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…

A short review of basic formulas from Hamiltonian formalism in classical mechanics in the case when Lagrangian contains N time-derivatives of n coordinate variables. For non-local models N=infinity.

The conformal equivalence of fourth-order gravity following from a non-linear Lagrangian L(R) to theories of other types is widely known, here we report on a new conformal equivalence of these theories to theories of the same type but with…

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…

Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…

An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian…

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…

One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched…

The Hamilton theories for higher orders classical Lagrange functions result on a well known Ostrogradski's instabilities. In this work, we propose a different definition for the second order canonical momentum and obtain a new set of second…

We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the…

We analyze the presumptions which lead to instabilities in theories of order higher than second. That type of fourth order gravity which leads to an inflationary (quasi de Sitter) period of cosmic evolution by inclusion of one curvature…

We review a perturbative approach to deal with Lagrangians with higher or infinite order time derivatives. It enables us to construct a consistent Poisson structure and Hamiltonian with only first time derivatives order by order in…

The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…

The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…

We propose a higher-order Skyrme model with derivative terms of eighth, tenth and twelfth order. Our construction yields simple and easy-to-interpret higher-order Lagrangians. We first show that a Skyrmion with higher-order terms proposed…

The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…

We consider certain analytical features of a stochastic model that can explain among other things competition among species and simultaneous predation on the competing species from a geometric perspective which allows for a systematic…

Dynamics generated from Hamiltonians enjoy potential pathways to quantisation, but standard Hamiltonians are only capable of generating conservative forces. Classes of Hamiltonians have been proposed in Berry et al. capable of generating…

We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…