相关论文: Average Angular Velocity
We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in phase space, the method of images and use of the classical diffusion equation. The…
Statistical average of the axial current is evaluated on the basis of the covariant Wigner function. In the resulting formula, chemical potential $\mu$, angular velocity $\Omega$ and acceleration $a$ enter in combination $\mu \pm (\Omega…
This paper sets out to explain: 1. Why the speed of light c is a constant and is the maximum speed at which any moving entity can travel. 2. Why time elapsed is different for a moving entity relative to a stationary entity. 3. Why there has…
This Letter, i.e. for the first time, proves that a general invariant velocity is originated from the principle of special relativity, namely, discovers the origin of the general invariant velocity, and when the general invariant velocity…
Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in…
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…
Inertial motion is considered in the plane of events characterized by the homogeneous Lorentz group L. On the basis of this group, a set of inertial movements and its decomposition into sets which are disconnected from one another with…
The dynamics of systems of multiple gravitationally interacting bodies is often studied in a frame attached to one of the objects (e.g. a central star in a planetary system). As this frame is generally non-inertial, indirect forces appear…
We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results, which display, in some cases, a gain of one full derivative.…
We derive the virial theorem appropriate to two-dimensional point vortices at statistical equilibrium in the microcanonical and canonical ensembles. In an unbounded domain, it relates the angular velocity to the angular momentum and the…
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can…
The Lorentz transformation is entirely derived from length contraction, itself established through the known light-clock thought experiment . This makes the derivation accessible to beginning students once Eintein's two postulates have been…
We consider a few thought experiments of radial motion of massive particles in the gravitational fields outside and inside various celestial bodies: Earth, Sun, black hole. All other interactions except gravity are disregarded. For the…
We discuss a constraint on the speed of sound, $c_s^2$, derived from relativistic kinetic theory and show how it can be expressed in terms of the average sound speed, $\langle c_s^2 \rangle$. This reformulation highlights the interplay…
We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary space-times. These expressions involve non-locally defined conformal factors. In certain…
In this manuscript, we consider the case where a Brownian particle is subject to a static periodic potential and is driven by a constant force. We derive analytic formulas for the average velocity and the effective diffusion.
While vorticity is the classical tool for analyzing rotational fluid kinematics, it inherently focuses on local, differential spin. This paper introduces a complementary framework based on the angular momentum density field, $\mathbf{L} =…
A neo-classical relativistic mechanics theory is presented where the spin of an electron is a natural part of its space-time path as a point particle. The fourth-order equation of motion corresponds to the same Lagrangian function in proper…
We calculate and verify with simulations the ratio between the average translational and rotational energies of systems with rough, inelastic particles, either forced or freely cooling. The ratio shows non-equipartition of energy. In…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…