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April 2nd, 2017, 02:14 PM   #1
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HELP: Special Relativity Addition of Velocities Trigonometry

Hello guys, can anyone help me to understand how Einstein arrives at the equation for V? I do not understand or know how he introduces the trigonometry.

2nd equation.jpg3rd equation.jpg
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April 3rd, 2017, 01:42 AM   #2
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Elementary ttreatments of relativity present the motions in the Lorenz transformation as being parallel to one of the axis (usually the x axis).

Of course more generally the motion may not be parallel, in which case trigonometry becomes involved.

This is also true of the Galilean/Newtonian transformation.

I can't read your extracts properly but I think your velocity is in the xy plane ie normal to the z axis so only the angles in the original and transformed coordinate system are involved. Life is more complicated in true 3D where the velocity is not parallel to any axis.

Note that when you compare velocities in two coordinate systems you are effectively adding the relative velocity between the coordinate systems, that is where the (vector) addition comes in.

The use of the hyperbolic tangent function leads to a property known as the rapidity, which can be used to replace the ordinary velocity and leads to simpler equations.

If you would like to post proper readable sized images I can comment in more detail, appropriate to your presentation.
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Last edited by studiot; April 3rd, 2017 at 02:21 AM.
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