Pilitron mechanics

Pilitron mechanics are the pilitron physics description of motion (and mass).

Notation and Laws
Speed and velocity are given by the speed parameter $$\bar{u}$$ and the velocity parameter $$\boldsymbol{\bar{u}}$$. Mass is defined by the mass parameter $$\bar{m}$$.

The pilitron laws of motion explain the mass and velocity of systems. It is the extension of already known laws.

First Law
The first pilitron law of motion states that the mass of a moving body is its rest mass multiplied by the Lorentz factor:


 * $$\bar{m} = \gamma m_0 = \frac{m_0}{\sqrt{1-\frac{\bar{u}^2}{c^2}}}$$

where:
 * m$0$ is the rest mass
 * is the Lorentz factor
 * c is the speed of light in vacuum

Second Law
The second pilitron law of motion states that the velocity of an object changes when forces are applied to it, according to the transformation:


 * $$\boldsymbol{\bar{u}}^{\prime} = \boldsymbol{\bar{u}} + \sum \frac{\mathbf{F}t}{\bar{m}}$$

where F is a force vector and t is the elapsing time.

Third Law
The third pilitron law of motion states that the mass of a rotating system can be defined by the sum of masses of the moving sub-systems:


 * $$\bar{m} = \sum_{d=0}^{r} \left(\sum \frac{m_0}{\sqrt{1-\frac{\left(2R\pi d \right)^2}{c^2}}} \right)$$

where:
 * r is the radius of the system
 * m$0$ is the rest mass of a particle at distance d away from center
 * R is the rotational speed of the system
 * c is the speed of light

The sum inside the brackets means the sum of masses of particles within the given circumference.

The rotational speed R is by definition the number of full turns per unit of time. The dimension is T-1.

Fourth Law
The fourth pilitron law of motion states that the speed of light c is caused by tension and vacuum resistance. This relates some physical constants:


 * $$c = \sqrt{\frac{\delta}{V_R}} = \sqrt{\frac{\delta\ell_P}{M_0}}$$

where:
 * c is the speed of light
 *  is the vacuum tension, ie. the quantum of force
 * VR is the vacuum resistance
 * M0 is the quantum of mass
 * $\ell$P is the Planck length