Related papers: Jerk and Hyperjerk in a Rotating Frame of Referenc…
Jerk plays a pivotal role in the thrilling experience of many amusemement park rides. In addition to exploring the physical aspect of jerks, we tackle the empirical observation of an attractive force between passengers in the popular…
This note is concerned with the problem of motion modeling in Physics. We aim to use the Time-Variant Local Autocorrelation Polynomial to understand the mathematical model of motion description. The mathematical explanation of the existence…
The relativistic jerk, snap and all higher-order kinematical D-vectors are defined for the motion of a massive particle in a D-dimensional Minkowski spacetime. We illustrate the formalism with stationary motions, for which we provide a new,…
We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…
Jerky active particles are Brownian self-propelled particles which are dominated by ``jerk'', the change in acceleration. They represent a generalization of inertial active particles. In order to describe jerky active particles, a linear…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
Whether a string has rotation and shear can be investigated by an anology with the point particle. Rotation and shear involve first covariant spacetime derivatives of a vector field and, because the metric stress tensor for both the point…
Formal definition of the reference frame is given. This definition is valid for nonrelativistic and relativistic cases. Proposed definition allows using wide classes of reference frames without restriction to inertial, uniformly accelerated…
A new derivation of the acceleration of a particle in a non-inertial reference frame, including the Coriolis effect, is developed using the geometry of complex numbers in the complex plane.
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
In motion Kinematics, it is well-known that the time derivative of a 3x3rotation matrix equals a skew-symmetric matrix multiplied by the rotation matrix where the skew symmetric matrix is a linear (matrix valued) function of the angular…
We discuss in Minkowski spacetime the differences between the concepts of constant proper $n$-acceleration and of vanishing $(n+1)$-acceleration. By $n$-acceleration we essentially mean the higher order time derivatives of the position…
The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than…
A human is a thing that moves in space. Like all things that move in space, we can in principle use differential equations to describe their motion as a set of functions that maps time to position (and velocity, acceleration, and so on).…
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to…
Physics of non-inertial reference frames is a generalizing of Newton's laws to any reference frames. The first, Law of Kinematic in non-inertial reference frames reads: the kinematic state of a body free of forces conserves and determinates…
Endomorphisms of the measure algebra of commutative hypergroups are investigated. We focus on derivations and higher order derivations which are closely related to moment function sequences of higher rank. We describe the exact connection…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
Originally introduced in connection with general relativistic Coriolis forces, the term $\textit{frame-dragging}$ is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently…
The general construction of extended refrence frames for noninertial observers in flat space is studied. It is shown that, if the observer moves inertially before and after an arbitrary acceleration and rotation, the region where reference…