Related papers: Lagrangians for biological models
Constrained optimization problems exist in many domains of science, such as thermodynamics, mechanics, economics, etc. These problems are classically solved with the help of the Lagrange multipliers and the Lagrangian function. However, the…
The applicability of advanced classical mechanics (viz., the Lagrangian and/or Hamiltonian approaches) to real-world problems may not always seem straightforward, despite the mathematical rigor and elegance of this field. Here, we present a…
Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of the principal modified equation and one additional equation…
In this paper, the theory of the fractional singular Lagrangian systems is investigated with second order derivatives. The fractional quantization for these systems is examined using the WKB approximation. The Hamilton Jacobi treatment can…
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…
We present two types of relativistic Lagrangians for the Lorentz-Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends…
We formulate higher order variations of a Lagrangian in the geometric framework of jet prolongations of fibered manifolds. Our formalism applies to Lagrangians which depend on an arbitrary number of independent and dependent variables,…
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…
Multiplicity results for solutions of various boundary value problems are known for dynamical systems on compact configuration manifolds, given by Lagrangians or Hamiltonians which have quadratic growth in the velocities or in the momenta.…
Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in…
We prove an extension of Yuan's Lemma to more than two matrices, as long as the set of matrices has rank at most 2. This is used to generalize the main result of [A. Baccari and A. Trad. On the classical necessary second-order optimality…
In an attempt to look for the root of nonstandard Lagrangians in the theories of the inverse variational problem we introduce a logarithmic Lagrangian (LL) in addition to the so-called reciprocal Lagrangian (RL) that exists in the…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a…
We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. We first present a simple counterexample where the original conditions…
Anti-selfdual Lagrangians on a state space lift to path space provided one adds a suitable selfdual boundary Lagrangian. This process can be iterated by considering the path space as a new state space for the newly obtained anti-selfdual…
We show that dualization of BF models to Stueckelberg-like massive gauge theories allows a non-Abelian extension. We obtain local Lagrangians which are straightforward extensions of the Abelian results.
This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…
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…
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…