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Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On…
We formulate equations of motion and conservation laws for a quantum many-body system in a co-moving Lagrangian reference frame. It is shown that generalized inertia forces in the co-moving frame are described by Green's deformation tensor…
Consider a deformable body immersed in an incompressible liquid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we investigate the motion of the body, calculate its…
Angular momentum balance is examined in the context of the electrodynamics of a spinning charged sphere, which is allowed to possess any variable angular velocity. We calculate the electric and magnetic fields of the (hollow) sphere, and…
We construct the Lagrangian formulation of a micro-structured spinning, dilating and shearing (deformable) test body, moving in arbitrary non-Riemannian backgrounds possessing all geometrical entities of curvature, torsion and…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…
We investigate dynamics of a self-propelled deformable particle under external field in two dimensions based on the model equations for the center of mass and a tensor variable characterizing deformations. We consider two kinds of external…
The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a…
When a solid body is freely rotating at an angular velocity ${\bf \Omega}$, the ellipsoid of constant angular momentum, in the space $\Omega_1, \Omega_2, \Omega_3$, has poles corresponding to spinning about the minimal-inertia and…
Deformed relativistic kinematics have been considered as a way to capture residual effects of quantum gravity. It has been shown that they can be understood geometrically in terms of a curved momentum space on a flat spacetime. In this…
The notion of inertial reference frame is abandoned and I replaced it by a local reference frame on which the fundamental law of mechanics is expressed. The distant interactions of cause and effect are modeled by the propagation of waves…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…
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…
We present a rigorous framework for determining equilibrium configurations of uniformly rotating self-gravitating fluid bodies. This work addresses the longstanding challenge of modeling rotational deformation in celestial objects such as…
We study the motion of the system, S, constituted by a rigid body, B, containing in its interior a viscous compressible fluid, and moving in absence of external forces. Our main objective is to characterize the long time behavior of the…
We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…
In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have…
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…
In this article we consider the affinely-rigid body moving in the three-dimensional physical space and subject to the Kirchhoff-Love constraints, i.e., while it deforms homogeneously in the two-dimensional central plane of the body it…