Related papers: On a kinematic proof of Andoyer variables canonici…
This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-body dynamics and presents some new results. As is well known, the problem of unsupported and unperturbed rigid rotator can be reduced. The availability of this…
Andoyer variables are well known for the study of rotational dynamics. These variables were derived by Andoyer through a procedure that can be also used to obtain the Hill variables of the Kepler problem. Andoyer construction can also…
An algebraic procedure of getting of canonical variables in a rigid body dynamics is presented. The method is based on using a structure of an algebra of Lie-Poisson brackets with which a Hamiltonian dynamics is set. In a particular case of…
Both orbital and rotational dynamics employ the method of variation of parameters. We express, in a non-perturbed setting, the coordinates (Cartesian, in the orbital case, or Eulerian in the rotation case) via the time and six adjustable…
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…
We use a canonical parametrization of twisted geometries describing the classical phase space of loop quantum gravity on a fixed graph, and establish its explicit correspondence with the associated frame bases and spinorial descriptions.…
We face the well-known gyrokinetic problem, which arises in the description of the dynamics of a charged particle subject to fast gyration for the presence of a strong electromagnetic field. The customary approach to gyrokinetic theory,…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
The gyrokinetic description of particle dynamics faces a basic difficulty when a special type of canonical variables is sought, i.e., the so-called \textit{gyrokinetic canonical variables}. These are defined in such a way that two of them…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
This note presents an attempt to provide a conceptual framework for variational formulations of classical physics. Variational principles of physics have all a common source in the {\it principle of virtual work} well known in statics of…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We…
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec \tau}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system.…
An explicit expression in terms of canonical variables is obtained for the Hamiltonian functional determining the fully nonlinear dynamics of two-dimensional potential flows of an ideal fluid with a free surface over an arbitrary nonuniform…
One of the fundamental postulates of the special relativity theory is existence of a single system of universal coordinate transforms for inertial reference frames, that is coordinate transforms, which are uniquely determined by space-time…
The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group…
It is well known that a rotation of a free generic three-dimensional rigid body is stationary if and only if it is a rotation around one of three principal axes of inertia. As it was noted by many authors, the analogous result is true for a…
Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the $d$ dimensional Riemann space-time. Theory of canonical transformations, which relate equivalent…