相关论文: The comfortable roller coaster -- on the shape of …
Analyzing the motion of a roller coaster allows for an instructive introduction of various theoretical concepts in a concrete and enjoyable context. We start by modeling the roller coaster train as a point particle. We then develop more…
In this paper we show all possible ramps where an object can move with constant speed under the effect of gravity and friction. The planar ramp are very easy to describe, just rotate a curve with velocity vector (tanh(as),sech(as)). Recall…
In this paper, I introduce general equation of conics sections based on physical problem on the earth surface in [1]. The conics sections here (hyperbola and ellips) are generated by all maximum points of parabolas. Based on it, I derived…
Mechanics texts tell us that a particle in a bound orbit under gravitational central force moves on an ellipse, while introductory physics texts approximate the earth as flat, and tell us that the particle moves in a parabola. The…
We analyse the motion of a sphere that rolls without slipping on a conical surface having its axis in the direction of the constant gravitational field of the Earth. This nonholonomic system admits a solution in terms of quadratures. We…
In the problem of cylinder rolling without slipping on a horizontal floor, both the cylinder and floor are generally treated as rigid bodies in normal textbooks. When the air resistance is ignored, the equation of motion has a solution with…
The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball's frame of reference. The normal…
The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or…
We investigate the problem of determining the planar curves that describe ramps where a particle of mass $m$ moves with constant-speed when is subject to the action of the friction force and a force whose magnitude $F(r)$ depends only on…
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
For geodesic motion of a particle in a stationary spacetime the $U_0$ component of particle 4-velocity is constant and is considered to be a conserved mechanical energy. We show that this concept of a conserved mechanical energy can be…
We discuss the existence and stability of circular orbits of a relativistic point particle moving in a central force field. The stability condition is somewhat more restrictive in Special Relativity. In the particular case of attractive…
The equation for the conic sections describing the possible orbits in a potential $V \sim r^{-1}$ is obtained by means of a vector constant of the motion differing from the traditional Laplace-Runge-Lenz vector.
A class of harmonic solutions to the steady Euler equations for incompressible fluids is presented in two dimensions in circular, elliptic and bipolar coordinates. Since the velocity field is solenoidal in this case, it can be written as…
The velocity field within a steady toroidal vortex is found for arbitrary mean core radius and section ellipticity. The problem is solved by transforming to coordinates that define invariant sets. The method allows the properties of the…
The trajectory and the orbital velocity are determined for an object moving in a gravitational system, in terms of fundamental and independent variables. In particular, considering a path on equipotential line, the elliptical orbit is…
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution…
We consider the slowly rotating relativistic stars with a uniform angular velocity in the scalar-tensor gravity, and examine the rotational effect around such compact objects. For this purpose, we derive a 2nd order differential equation…
A classical problem of mechanics involves a projectile fired from a given point with a given velocity whose direction is varied. This results in a family of trajectories whose envelope defines the border of a 'safe' domain. In the simple…
Paper strips, e.g. confetti, descending to the floor begin to rotate around the horizontal axis after a short time. This slows down the vertical velocity compared to free fall and adds a horizontal velocity component. The frequency of…