Related papers: Complex Lagrangian dynamics
The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of…
Using Grassmann variant of classical mechanics, we construct Lagrangian dynamics of classical spinning particle in (possibly non-abelian) gauge fields. Quantization of this model is briefly discussed.
The problems that are connected with Lagrangians which depend on higher order derivatives (namely additional degrees of freedom, unbound energy from below, etc.) are absent if effective Lagrangians are considered because the equations of…
The aim of this study is to introduce quaterinon Kaehler analogue of Lagrangian mechanics. Finally, the geometric and physical results related to quaternion Kaehler dynamical systems are also presented.
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
A geometric global formulation of the higher-order Lagrangian formalism for systems with finite number of degrees of freedom is provided. The formalism is applied to the study of systems with groups of Noetherian symmetries.
Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry, among others. In recent years there has been a great…
An alternative class of the Lagrangian called the multiplicative form is suc- cessfully derived for a system with one degree of freedom for both non-relativistic and relativistic cases. This new Lagrangian can be considered as a…
I show how Hamilton's philosophical commitments led him to a causal interpretation of classical mechanics. I argue that Hamilton's metaphysics of causation was injected into his dynamics by way of a causal interpretation of force. I then…
A direct reformulation of the Hamiltonian formalism in terms of the intrinsic geometry of infinitely prolonged differential equations is obtained. Concepts of spatial equation and spatial-gauge symmetry of a Lagrangian system of equations…
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…
Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase…
This note gives an introduction to Lagrangian field theories in the presence of boundaries. After an overview of the classical aspects, the cohomological formalisms to resolve singularities in the bulk and in the boundary theories (the BV…
In this study, Lagrangian and Hamiltonian systems, which are mathematical models of mechanical systems, were introduced on the horizontal and the vertical distributions of tangent and cotangent bundles. Finally, some geometrical and…
In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the…
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…
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…