Related papers: Scope of the action principle
We report a gravitational $BF$-type action principle propagating two (complex) degrees of freedom that, besides the gauge connection and the $B$ field, only employs an additional Lagrange multiplier. The action depends on two parameters and…
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 dual formalism for Lagrange multipliers is developed. The formalism is used to minimize an action function $S(q_2,q_1,T)$ without any dynamical input other than that $S$ is convex. All the key equations of analytical mechanics -- the…
Consistent interactions that can be added to a free, Abelian gauge theory comprising a finite collection of BF models and a finite set of two-form gauge fields (with the Lagrangian action written in first-order form as a sum of Abelian…
The least action principle, through its variational formulation, possesses a finalist aspect. It explicitly appears in the fractional calculus framework, where Euler-Lagrange equations obtained so far violate the causality principle. In…
The invariance theorems obtained in analytical mechanics and derived from Noether's theorems can be adapted to fluid mechanics. For this purpose, it is useful to give a functional representation of the fluid motion and to interpret the…
Relativistic systems of particles interacting pairwise at a distance (interactions not mediated by fields) in flat spacetime are studied. It is assumed that the interactions propagate at the speed of light in vacuum and that all masses are…
The loop variable approach used earlier to obtain free equations of motion for the massive modes of the open string, is generalized to include interaction terms. These terms, which are polynomial, involve only modes of strictly lower mass.…
The dynamics of some non-conservative and dissipative systems can be derived by calculating the first variation of an action-dependent action, according to the variational principle of Herglotz. This is directly analogous to the variational…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…
This paper discusses some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
A way to obtain a correspondence between the first order and second order formalism is studied. By introducing a Lagrange multiplier coupled to the covariant derivative of the metric, a metricity constraint is implemented. The new…
We want to unify usual equation of motion laws of nature with "laws" about initial conditions, second law of thermodynamics, cosmology. By introducing an imaginary part -- of a similar form but different parameters as the usual real part --…
In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how…
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…
We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for…
In this paper we work out the explicit form of the change of variables that reproduces an arbitrary change of gauge in a higher-order Lagrangian formalism.
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This work shows that the procedure of deriving…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…