The second property determines the length of the global vector of acceleration \(\mathbf{R}'_t\), which is obtained by differentiating at the time of the global velocity vector: \[|\mathbf{R}'(t)| = {\beta'(t) \over 1 - \beta(t)^2}, \quad \beta(t) = {v(t) \over c} \qquad (3.1)\] the Following property is very unusual and stems from the previous one.

We prove that the integral of the module of global acceleration equal to the "speed" or "Hyper speed" [1]. This will printeriem the formula (3.1): \[\int \limits_0^t |\mathbf{R}'(t)| \Bbb{d}t = \int \limits_0^t {\beta'(t) \Bbb{d}t \over 1 - \beta(t)^2} = \int \limits_0^t {\Bbb{d}\beta(t) \over 1 - \beta(t)^2} \qquad (3.2)\] Such a Intergal table [2] and is taken as \[\int \limits_0^t {\Bbb{d}\beta(t) \over 1 - \beta(t)^2} = \frac12 \ln{1 + \beta(t) \over 1 - \beta(t)} \qquad (3.3)\] As we rememberto get the real global vector, velocity, or acceleration, \(\mathbf{R}\) or \(\mathbf{R}'_t\) you need to multiply by \(c\). In this case we get Lorenceau "speed"=> \[\frac{c}{2} \ln{1 + \beta(t) \over 1 - \beta(t)} = \theta \qquad (3.4)\] the Third property is proved.

Speed [1] used in physics, when necessary, for example, to go from low velocity to a large — close to the speed of light. Then instead of the usual speed is substituted for its relativistic counterpart is speed. But in an isolated space problems, no jumping, at all speeds its global vector has the same form. As we can see, using a single space, we can obtain the necessary relativistic formula is quite simple methods, while it does not use imaginary coordinates or angles!