- #1
Identity
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In a lecture on special relativity online, the form
[tex]x'=x\cosh{\omega}-ct\sinh{\omega}[/tex]
[tex]t'=-x\sinh{\omega}+ct\cosh{\omega}[/tex]
is used for the lorentz transformations, where the velocity is [tex]v=\frac{c\sinh{\omega}}{\cosh{\omega}}[/tex].
However, I'm wondering, couldn't you also do
[tex]x'=x\sec{\omega}-ct\tan{\omega}[/tex]
[tex]t'=-x\tan{\omega}+ct\sec{\omega}[/tex]
(or even the similar thing with [tex]\csc{\omega}[/tex] and [tex]\cot{\omega}[/tex])
With [tex]v=\frac{c\tan{\omega}}{\sec{\omega}}[/tex]
Since this also reproduces the lorentz transformations
Is there any advantage to using the hyperbolic functions instead?
[tex]x'=x\cosh{\omega}-ct\sinh{\omega}[/tex]
[tex]t'=-x\sinh{\omega}+ct\cosh{\omega}[/tex]
is used for the lorentz transformations, where the velocity is [tex]v=\frac{c\sinh{\omega}}{\cosh{\omega}}[/tex].
However, I'm wondering, couldn't you also do
[tex]x'=x\sec{\omega}-ct\tan{\omega}[/tex]
[tex]t'=-x\tan{\omega}+ct\sec{\omega}[/tex]
(or even the similar thing with [tex]\csc{\omega}[/tex] and [tex]\cot{\omega}[/tex])
With [tex]v=\frac{c\tan{\omega}}{\sec{\omega}}[/tex]
Since this also reproduces the lorentz transformations
Is there any advantage to using the hyperbolic functions instead?