Related papers: Understanding the Hamiltonian Function through the…
We take advantage of different generalizations of the tangent manifold to the context of graded manifolds, together with the notion of super section along a morphism of graded manifolds, to obtain intrinsic definitions of the main objects…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…
It is shown that any singular Lagrangian theory: 1) can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; 2) leads to a special kind of nonabelian gauge theory which is similar…
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…
Hamilton equations based not only upon the Poincare--Cartan equivalent of a first-order Lagrangian, but rather upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton--De Donder theory, but…
Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have found attention in the literature. For one thing, such Lagrangians have deep connections with several aspects of nonlinear dynamics including…
The task of finding a consistent relationship between a quantum Hamiltonian and a classical Lagrangian is of utmost importance for basic, but ubiquitous techniques like canonical quantization and path integrals. Nonconvex kinetic energies…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
In classical mechanics, we can describe the dynamics of a given system using either the Lagrangian formalism or the Hamiltonian formalism, the choice of either one being determined by whether one wants to deal with a second degree…
We explore a hybrid expansion of the disturbing function in planetary dynamics that combines elements of the classical Laplace and Legendre developments. This formulation retains the structure of the Laplace expansion, but expresses the…
In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and…
After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…
It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
In this paper we study a Hamiltonization procedure for mechanical systems with velocity-depending (nonholonomic) constraints. We first rewrite the nonholonomic equations of motion as Euler-Lagrange equations, with a Lagrangian that follows…
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \emph{Fuzzy Dynamics} of…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
The partial derivative of the kinetic energy of a dynamical system with respect to a generalized coordinate as it appears in the Lagrangian formalism is not equal to the derivative of the kinetic energy with respect to the same coordinate…
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…
The connection between the Hamilton and the standard Lagrange formalism is established for a generic Quantum Field Theory with vanishing vacuum expectation values of the fundamental fields. The Effective Actions in both formalisms are the…