Planar motion with Fresnel integrals as components of the velocity

Flores-Garduno, E.; Mancas, Stefan C.; Rosu, H. C.; Perez-Maldonado, M.

doi:10.31349/revmexfis.66.585

Cited by 1 publication

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References 7 publications

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“…Such models are used in chaos theories. More generally, in classical physics, the Jerk dynamics have been studied in specific two-and three-dimensional cases such as [10][11][12], and its applications have been investigated in crystals with memory [13], geomagnetic Jerks [14] and other chaotic systems [15]. We also mention the famous example of a third-order equation of motion in classical electrodynamics as embodied by the Lorentz-Dirac equation of the relativistic electron [16], which is closer to the hyperbolic Jerk that we discuss here.…”

Section: The Four-jerkmentioning

confidence: 99%

Relativistic hyperbolic motion and its higher order kinematic quantities

Perez-Roman¹,

Rosu

2022

Rev. Mex. Fís.

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We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1+1 and 1+3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up to the fourth proper time derivative (the Snap). In the 1 + 3 case, following a recent work of Pons and de Palol [Gen. Rel. Grav. 51 (2019) 80], a vectorial differential equation for the acceleration is obtained which by considering constant proper acceleration is turned into a nonlinear second order differential equation in terms of derivatives of the radius vector. If, furthermore, the velocity is parameterized in terms of hyperbolic functions, one obtains a differential equation to solve for the argument f(s) of the velocity. Differently from Pons and de Palol, who employed the particular solution, linear in the proper time s, we obtain the general solution and use it to work out more general expressions for the kinematical quantities. As a byproduct, we obtain a class of modified Rindler hyperbolic worldlines characterized by supplementary contributions to the components of the kinematical quantities.

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