Invariant Transformation between Vector & Scalar Interpretation of the Particle

Kartazion · « **Reply #40 on:** 08/08/2022 05:58:18 »

Abridge:

In the case of a particle bound to gravity; it is logical to say that when the kinetic energy due to an impulse on the particle has in:
- 1 a great momentum until 0
- 2 an depletion of the kinetic energy until 0 at the point where it falls back.

IOW upon depletion of kinetic energy is then accumulated potential energy. Which means that when KE decreases PE increases proportionally and vice-versa.

The amplitude of y at x=0 gives the momentum of the impulse. Once the impulse given and in the case of a gravitational oscillator in the vacuum, then the motion is perpetuated.

The arrows cathetus and hypotenuse according to their direction and their length determine all the necessary information relating to the particle; namely the energies at time t, the exact position, the impulse momentum, the momentum of the particle, the speed, ... Only the mass of the particle and the total distance of x must be predefined as a value. The frequency of oscillation of the oscillator then gives the total energy density of the system by the mass of the particle.

Kartazion · « **Reply #41 on:** 08/08/2022 17:22:42 »

If we want to keep the exactness of density-energy through an harmonic oscillator SHO in the proportionality between KE and PE as well as the good sense of direction of the arrow of its angular rotation; then in Figure 1 the exact corrective in graph. I imagine that this conventional model Figure 2 is a little obsolete following that of the new gravitational oscillator which brings the total energy state back to 0. The problem of the Figure 2 is that it does not take into account the negativity of y and represent only the energy of the potential well contrary to the energy density. In Figure 2 a clock cannot therefore be applied.

Figure 1.

Figure 2.

Here we have evidence of a new and very simple model to study for first-year students and up.

While waiting for relevant questions, I wish you a good evening.