# Integration of Lorentz Factor

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1. Dec 14, 2015

### Astro Boy 327

Just for my own entertainment I integrated the Lorentz factor with respect to velocity, using basic trig sub, I got the equation arcsin(v/c)*(mc^2). What does this mean? Is it just useless and irrelevant in the physics world or does it have some sort of hidden meaning?

2. Dec 15, 2015

### Orodruin

Staff Emeritus
I do not know where you got the mass from, there is no mass in the gamma factor nor in the velocity. Regardless, it does not a priori have any physical meaning to integrate the gamma factor wrt velocity.

3. Dec 15, 2015

### Ibix

Not sure what you mean by the Lorentz factor here. If I'm not mistaken you have integrated $\int_0^v \gamma (v')mcdv'$. I'm not quite sure why you would want to do this.

Hyperbolic functions do turn up quite frequently when integrating velocities and the like in Special Relativity, which is a consequence of the structure of Minkowski space time. You might like to look up "rapidity".