相关论文: Equations of Motion of Systems with Internal Angul…

We compute explicitly the equations of motion of the Hamiltonian formulation of quadratic gravity. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor. We employ the symbolic…

We revisit the problem of the equations of motion of a system of $N$ self-interacting massive particles (without spins) in the first post-Minkowskian (1PM) approximation of general relativity. We write the equations of motion, gravitational…

Optical intrinsic angular momentum can be regarded as derivation from spatial superposition of optical vector fields embodied by spinning or and spiraling the electric field vector. We employ vectorial formulation derivation to…

Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory one…

The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…

We examine the angular momentum transport properties of disks composed of macroscopic particles whose velocity dispersions are externally enhanced (``stirred''). Our simple Boltzmann equation model serves as an analogy for unmagnetized…

The angular momentum, angular velocity, Kelvin circulation, and vortex velocity vectors of a quantum Riemann rotor are proven to be either (1) aligned with a principal axis or (2) lie in a principal plane of the inertia ellipsoid. In the…

Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…

In geometric algebra, the rotation of a vector is described using rotors. Rotors are phasors where the imaginary number has been replaced by a oriented plane element of unit area called a unit bivector. The algebra in three dimensional…

Angular momentum is traditionally taught as a (pseudo)vector quantity, tied closely to the cross product. This approach is familiar to experts but challenging for students, and full of subtleties. Here, we present an alternative pedagogical…

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…

Approximate equations are derived for the motion of a gyroscope on the earth's gravitational field using the Einstein, Infeld, Hoffmann surface integral method. This method does not require a knowledge of the energy-momentum-stress tensor…

A new approach has been used to evaluate the momentum and angular momentum of the isotropic and homogeneous cosmological models. It is shown that the results obtained for momentum exactly coincide with those already available in the…

By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital…

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…

Euler-Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two-spheres. The geometric structure of a product of two-spheres is carefully considered in order to obtain global…

Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…

We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…

We propose a geometrical approach to the mechanics of continuous media equipped with inner structures and give the basic (mass conservation, Navier-Stokes and energy conservation) equations of their motion.

The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…