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, Lorentz covariant, classification. We generalize some cases to branes, explaining the relevance to uniform motion in a heat bath. We also consider some non-...

In literature many chaotic systems, based on third-order jerk equations with different nonlinear functions, are available. A jerk system is taken to be a part of dynamical systems that can exhibit regular and chaotic behavior. By extension, a hyperjerk system can be described as a dynamical system with nth-order ordinary differential equations where n is 4 or up to. Hyperjerk systems have been ...

The human limiting values for sudden accelerations we have determined can be used to evaluate specific physical conditions that cause problems in maintaining postural balance. A comparison between the data obtained in the laboratory and the situations occurring during public transport by tram, bus, and metro revealed that both the initial impetus ("jerk") and the level of acceleration found in ...

Abstract Following the observed pattern of a new geomagnetic jerk every 3–4 years, certain predictions suggested that event should occur around 2020 after one 2017.5. In this work, we explore scenario by analysing secular variation East field component in both ground and satellite data. At ground, use available data from 2015 to 2021 10 observatories worldwide distributed. This analysis shows o...

In this investigation, an (un)forced third-order/jerk Van-der Pol oscillatory equation is solved using two perturbative methods called the Krylov–Bogoliúbov–Mitropólsky method and multiple scales method. Both first- second-order approximations for unforced forced jerk equations are derived in detail proposed methods. Comparative analysis performed between analytical numerical fourth-order Runge...

The parallel connection of technical and biological systems with a comparable mechanical behavior offers the possibility reducing interaction forces between those systems. Especially in context human–robot (e.g., exoskeletons), it can improve user safety acceptance at same time. With this aim, we used antagonistic actuators nonlinear compliance for modular upper-extremity exoskeleton following ...

Investigations of one hand reaching tasks suggest that humans use some optimal criterion to select the trajectory for the motion. In this paper, the minimum jerk model that was proposed to account for single-hand reaching tasks is extended to the two-arm case. A set of experiments was performed to verify the model. The repeatability of the experimental results was investigated. The data shows t...

The problem of designing jerk limited-time optimal control proŽ les for rest-to-rest maneuvers of  exible structures with multiple actuators is addressed. The problem formulation includes constraints to cancel the poles corresponding to the rigid-body mode and  exible modes of the system and to satisfy the boundary conditions of the rest-to-rest maneuver. Further constraints can be added to i...