Related papers: The dynamics of a rotating ellipsoid
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…
This paper considers the motion control of a particle and a spinning disc on rotating earth. The equations of motion are derived using Lagrangian mechanics. Trajectory planning is studied as an optimization problem using the method referred…
In this review, we describe the physical processes driving the dynamical evolution of binary stars, namely the circularization of the orbit and the synchronization of their spin and orbital rotation. We also discuss the possible role of the…
The turnaround epoch of gravitational collapse is examined by means of relativistic Lagrangian perturbation theory. Averaged, scalar equations applied to the fluid's evolution reveal some scale-independent universality of parameters for a…
The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered.…
The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
Among pebbles strewn across a sandy ocean beach one can find relatively many with a nearly perfect elliptical (ellipsoidal) shape, and one wonders how this shape was attained and whether, during abrasion, the pebbles would remain elliptical…
The equations of motion for the position and spin of a classical particle coupled to an external electromagnetic and gravitational potential are derived from an action principle. The constraints insuring a correct number of independent spin…
We study the classical electrodynamics of extended bodies. Currently, there is no self-consistent dynamical theory of such bodies in the literature. Electromagnetic energy-momentum is not conserved in the presence of charge and some…
We briefly review the foundations of a new relativistic fluid dynamics framework for polarized systems of particles with spin one half. Using this approach we numerically study the dynamics of the spin polarization of a rotating medium…
The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope…
In this paper we analyze the spinning motion of the hovering magnetic top. We have observed that its motion looks different from that of a classical top. A classical top rotates about its own axis which precesses around a vertical fixed…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
It is now known that the equations of motion for the contact point during peeling of an adhesive tape mounted on a roll introduced earlier are singular and do not support dynamical jumps across the two stable branches of the peel force…
We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being…
A complete, straightforward and natural Lagrangian description is given for the classical non-relativistic dynamics of a particle with colour or internal symmetry degrees of freedom moving in a background Yang-Mills field. This provides a…
The tilt-over mode in a precessing triaxial ellipsoid is studied theoretically and numerically. Inviscid and viscous analytical models previously developed for the spheroidal geometry by Poincar\'e [Bull. Astr. 27, 321 (1910)] and Busse [J.…
A simple derivation of an explicitly rotational invariant Lagrangian describing the dynamics of an antiferromagnetic spin system is presented. The scope of the derived Lagrangian is analysed in the context of schematic models. It is shown…