相关论文: Projective dynamics and classical gravitation

We take points and planes as fundamental, lines as derived, in an axiomatic formulation of three-dimensional projective space, the self-dual nature of which formulation renders automatic the principle of duality.

We define polygonal dynamics as a family of dynamical systems acting on points in projective spaces. The most famous example is the pentagram map. Similar collapsing phenomena seem to occur in most of these systems. We prove it in some…

Following recent work, this manuscript clarifies what the Gauss-Appell principle determines in incompressible, inviscid flow and how it connects to classical projection methods. At a fixed time, freezing the velocity and varying only the…

The Clausius Virial theorem of Classical Kinetic Theory is used to evaluate the pressure of a suspension of small particles at equilibrium in an isotropic homogeneous and stationary turbulent flow. It then follows a similar approach to the…

We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…

Hamiltonian dynamics of gravitational field contained in a spacetime region with boundary $S$ being a null-like hypersurface (a wave front) is discussed. Complete Hamiltonian formula for the dynamics (with no surface integrals neglected) is…

Induced dynamics is defined as dynamics of real zeros with respect to $x$ of equation $f(q_1-x,\ldots,q_N-x,p_1,\ldots,p_N)=0$, where $f$ is a function, and $q_i$ and $p_j$ are canonical variables obeying some (free) evolution. Identifying…

A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases…

Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…

A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…

It is shown, that by means of a special projection operator, the Liouville equation for an N-particle distribution function of classical particles, driven from an equilibrium state by an external field, can be exactly converted into a…

We provide exposition into the field of projection theory, which lies at the intersection of incidence geometry and geometric measure theory. We first give the necessary preliminaries in Chapter 2, focusing on incidences between points and…

We consider the simplest case of Rutherford scattering, i.e. the head-on collision, where the projectile is treated quantum mechanically. The convexity of repulsive Coulomb force invokes a disagreement between the Ehrenfest's and Hamilton's…

The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. The book begins with a brief review of relativity,…

In a full 3D context, we study a projectile subject to linear drag, a non-uniform gravitational field, time-dependent wind, and parameterized atmospheric thinning. In this general context, we provide integral solutions, exact to $\mathcal{…

The mantra about gravitation as curvature is a misnomer. The curvature tensor for a standard of rest does not describe acceleration in a gravitational field but the \underline{gradient} of the acceleration (e.g. geodesic deviation). The…

Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…

A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. Analytic approach is used for investigation.…

In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…