Related papers: Equations of Motion of Systems with Internal Angul…

The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. The controlled equations of motion are solved numerically using a predictor-corrector…

We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient…

This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…

Angular momentum has recently been defined as a surface integral involving an axial vector and a twist 1-form, which measures the twisting around of space-time due to a rotating mass. The axial vector is chosen to be a transverse,…

Four expressions involving sums of position and velocity coordinates bounding the total angular momentum of particle systems, and by extension of any continuous or discontinuous material systems, are derived which are tighter for any…

We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…

Differential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is also known as a rotation vector or axis-angle vector. The…

We derive the equations of motion of an extended test body in the context of Einstein's theory of gravitation. The equations of motion are obtained via a multipolar approximation method and are given up to the quadrupolar order. Special…

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…

Starting from Schr\"odinger's equation, Hamilton's classical equations of motion emerge from the collapse of the unsymmetrized wave function in a decoherent open quantum system entangled with its environment.

A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…

We consider geometric variational problems for a functional defined on a curve in three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange…

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…

We investigate the consistency of the fundamental governing equations of motion in continuum mechanics. In the first step, we examine the governing equations for a system of particles, which can be considered as the discrete analog of the…

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.…

We discuss the equation of motion of the rotating homogenous and isotropic model of the Universe. We show that the model predicts the presence of a minimum in the relation between the mass of an astronomical object and its angular momentum.…

It is shown that due to Thomas precession, angular momentum is not generally a constant of the motion in a quasiclassical model of the Positronium atom consisting of circular-orbiting point charges with intrinsic spin and associated…

Motion of a point mass in gravitational fields of the Sun and of the galactic disk is studied. Fundamental features of the motion are found by investigating the time-averaged differential equations for orbital evolution. Several types of…

It is well-known that an electric charge under a uniform magnetic field has a bidimensional motion if its initial position and velocity are perpendicular to this magnetic field. Although some constants of motion, as the energy and angular…