Related papers: Cartesian approach for constrained mechanical syst…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
A detailed program is proposed in the Lagrangian formalism to investigate the dynamical behavior of a theory with singular Lagrangian. This program goes on, at different levels, parallel to the Hamiltonian analysis. In particular, we…
Orbital motion of a body can be found from Newtonian equation of motion. However, it is useful to express the motion through time derivatives of Keplerian orbital elements, mainly if the motion is perturbed by small perturbing force. The…
We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle…
The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. This is done by choosing the reference system in one of the bodies which allows to…
These are pedagogical notes on the Hamiltonian formulation of constrained dynamical systems. All the examples are finite dimensional, field theories are not covered, and the notes could be used by students for a preliminary study before the…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
The Lagrange--Poincar\'e equations for the mechanical system describing the motion of a scalar particle on a Riemannian manifold with a given free and isometric action of a compact Lie group is obtained. In an arising principle fibre…
We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system…
The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
Individual-machine, superimposed-machine and equivalent-machine can be seen as the three major perspectives of the power system transient stability. In this paper, the machine paradigms are established according to the common thinking among…
In this paper we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical…
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations…
Starting from a suggestion of Einstein on the construction of the concept of space, we elaborate an intrinsic method to obtain space and time transformations between two inertial spaces of reference, mathematically modeled as affine…
This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…