Related papers: Lambda-symmetries of Dynamical Systems, Hamiltonia…
For an autonomous system the symmetries of the Lagrangian are embedded in the symmetries of the differential equation. Recently, it has been found that the modified Emden-type equations follow from non-standard Lagrangian functions which…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary…
This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion…
This paper explores the relationship between Cartan symmetries, dynamical similarities, and dynamical symmetries in contact Hamiltonian mechanics. By introducing an alternative decomposition of vector fields, we characterize these…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of…
Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate…
Equations of motion for a general relativistic post-Newtonian Lagrangian approach mainly refer to acceleration equations, i.e. differential equations of velocities. They are directly from the Euler-Lagrangian equations, and usually have…
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…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
The aim of this note is to discuss the relation between one-parameter continuous symmetries of the dynamics, defined on physical grounds, and conservation laws. In the Hamiltonian formulation, such symmetries of the dynamics in general…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
Ermakov systems possessing Noether point symmetry are identified among the Ermakov systems that derive from a Lagrangian formalism and, the Ermakov invariant is shown to result from an associated symmetry of dynamical character. The Ermakov…
There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we…
The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and…
We study in the Hamiltonian framework the local transformations $\delta_\epsilon q^A(\tau)=\sum^{[k]}_{k=0}\partial^k_\tau\epsilon^a{} R_{(k)a}{}^A(q^B, \dot q^C)$ which leave invariant the Lagrangian action: $\delta_\epsilon S=div$.…
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…
A hybrid framework is developed that highlights and unifies the most important aspects of the Noether correspondence between symmetries and conserved integrals in Lagrangian and Hamiltonian mechanics. Several main results are shown: (1) a…