Related papers: An extended Lagrangian formalism
A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…
We determine the most general scalar field theories which have an action that depends on derivatives of order two or less, and have equations of motion that stay second order and lower on flat space-time. We show that those theories can all…
In seeking a minimal variational formulation of Maxwell's equations, one is led naturally to the scalar and vector potentials as "adjoint" functions in a well-defined sense and to the crucial minus sign that defines the Lagrangian.
We construct the Hamiltonian formalism of bigravity for the potential of a general form. We find conditions on this potential and prove that under these conditions the formalism is equivalent to the one constructed with the celebrated…
It is well known that the equations of motion obtained from Newtons second law of motion can be obtained from a Lagrangian via the Euler-Lagrangian formulation if and only if the equations of motion satisfy the Helmholtz conditions. In this…
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…
We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that…
In this note we present invariant formulation of the d'Alambert principle and classical time-dependent Lagrangian mechanics with holonomic constraints from the perspective of moving frames.
Classically time is kept fixed for infinitesimal variations in problems in mechanics. Apparently, there appears to be no mathematical justification in the literature for this standard procedure. This can be explained canonically by…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this…
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…
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…
Enlarging on Parts I and II we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of full dynamic equations, including equations where the medium is moving or otherwise changing…
Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) for each second-order Lagrangian density on an arbitrary fibred manifold $p\colon E\to N$ the Poincar\'e-Cartan form of which is…
Loop corrections induce a dependence on the momentum squared of the coefficients of the Standard Model Lagrangian, making highly non-trivial (or even impossible) the diagonalization of its quadratic part. Fortunately, the introduction of…
Through duality it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or…
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under…
A proof is given for the observation that the equations of motion for the companion Lagrangian without a square root, subject to some constraints, just reduce to the equations of motion for the companion Lagrangian with a square root in one…
We introduce a Lagrangian which can be varied to give both the equation of motion and world-line deviations of spinning particles simultaneously.