Related papers: Constant Speed Ramps
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…
A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the…
The speed of a ball rolling without skidding or spinning on a surface $S$ is the length of the velocity of its center. We show that if the speed depends only on $p\in S$, then $S$ has constant mean curvature; and, conversely, that if the…
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…
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. The physical interpretation of the notion of relative acceleration is discussed. The notions of deformation acceleration, shear…
In relativity and quantum field theory, the vacuum speed of light is assumed to be constant; the range of validity of general relativity is determined by the Planck length. However, there has been no convincing theory explaining the…
We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor…
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…
We present the concept of speed maps: speed limits for mobile robots in human environments. Static speed maps allow for faster navigation on corridors while limiting the speed around corners and in rooms. Dynamic speed maps put limits on…
While the constant radial acceleration problem is known to be integrable and has received some recent attention in an orbital mechanics context, a closed form explicit solution, relating the state variables to a time parameter, has eluded…
Minimum-time speed profiles are constructed for planar paths with smooth strictly-monotonic signed curvature, subject to constraints on velocity, normal acceleration and tangential acceleration. The construction is explicit and exact, and…
We consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk…
Theories proposing a varying speed of light have recently been widely promoted under the claim that they offer an alternative way of solving the standard cosmological problems. Recent observational hints that the fine structure constant may…
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…
A family of plane oriented continuous paths depending on a fixed real positive number $R$ is considered. For any point $x$ on the path, the previous points lie out of any circle of radius $R$ having at $x$ interior normal in a suitable…
In the theory of differential geometry curves, a curve is said to be of constant-ratio if the ratio of the length of the tangential and normal components of its position vector function is constant. In this paper, we study and characterize…
A novel, interesting class of scalar-tensor gravity theories is those with a limit on the field motion, where the scalar field either goes to a constant acceleration or stops accelerating and goes to a constant velocity. We combine these…
In relativistic dynamics, force and acceleration are no longer parallel. In this article, we revisit the relativistic motion of a particle under the action of a constant force, $\boldsymbol{f}$. \ For a two-dimensional motion, the final…
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. The physical interpretation of the notion of relative velocity is discussed. The notions of deformation velocity tensor, shear…
We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation $\mathbf{F}=\frac{d\mathbf{p}}{dt}$, where $\mathbf{F}$ is the 3D force and $\mathbf{p}=m_0\gamma\mathbf{v}$ is…