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The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…
We present an analytical solution of a highly magnetized jet/wind flow. The left side of the general force-free jet/wind equation (the "pulsar" equation) is separated into a rotating and a nonrotating term. The two equations with either…
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points…
This article describes four innovative pedagogical exercises: (i) The expression for relation between cross sections in the laboratory and the centre of mass systems provided in text books assumes zero or low Q values which needs to be…
We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a…
We propose geometric tools that are suitable for studying the behavior of a billiard trajectory in a homogeneous force field. Two examples are considered: a vertical plane with an open top and with a parabolic or right angle boundary at the…
Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
We discuss a role of a momentum vector in the description of dynamics of systems with variable mass, and show some ambiguity in expressing the 2nd Newtonian law of dynamics in terms of momentum change in time for variable-mass systems. A…
We investigate the influence of the quadrupole moment of a rotating source on the motion of a test particle in the strong field regime. For this purpose the Hartle-Thorne metric, that is an approximate solution of vacuum Einstein field…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
The supersonic motion of gravitating objects through a gaseous medium constitutes a classical problem in theoretical astrophysics. Its application covers a broad range of objects and scales from planets up to galaxies. Especially the…
In this note, we provide explicit expressions for the projections onto the graph of a quadratic polynomial. The projections are obtained by examining the critical points of the associated quartic polynomial, that is, the roots of the cubic…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
Spherically symmetric hydrodynamical outflows accelerated thermally in the vicinity of a compact object are studied by generalizing an equation of state with a variable effective polytropic index, appropriate to describe relativistic…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…