Lorentz transform for acceleration

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SUMMARY

The discussion focuses on deriving acceleration (a) from velocity (v) using the Lorentz transformation equations. The key equation presented is u = (u - v) / (1 - vu/c²), where u represents velocity in the +x direction. Participants emphasize the need to differentiate both v and t within the Lorentz transformations to obtain the expression for acceleration in an accelerated frame. The process involves dividing the differential equation for dv by that for dt and simplifying the result.

PREREQUISITES
  • Understanding of Lorentz transformations
  • Familiarity with calculus, specifically differentiation
  • Knowledge of special relativity concepts
  • Basic grasp of velocity and acceleration definitions
NEXT STEPS
  • Study the derivation of Lorentz transformations in detail
  • Learn about differentiating functions in the context of special relativity
  • Explore the implications of acceleration in non-inertial frames
  • Investigate the relationship between velocity and acceleration in relativistic physics
USEFUL FOR

Physicists, students of relativity, and anyone interested in the mathematical foundations of acceleration in relativistic contexts.

mntb
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derivating a from v (lorentz transform)
u is the velocity in the +x direction
u=(u-v)/(1-vu/c^2)

a=du/dt

dt=I know
du=?
 
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Differentiate [tex]v[/tex] and also [tex]t[/tex] in the Lorentz transformations, divide the equation for [tex]dv[/tex] by the equation for [tex]dt[/tex] and simplify, you should be able to get the expression for the acceleration in an accerated frame.
 

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